# Mathematical Sciences Research Institute

Home > Scientific > Colloquia & Seminars > All Colloquia & Seminars > Past

1. # Geroch Lunch Seminar

Location: MSRI: Baker Board Room

The speaker will be chosen among the members of the audience at the time of the event. One or more volunteers from the audience will present a current topic of research, possibly but not necessarily one on which they are currently working.

Updated on Sep 16, 2013 02:56 PM PDT
2. # OT Programmatic Seminar: Geometry of Wasserstein space

Location: MSRI: Baker Board Room
Speakers: John Lott (University of California, Berkeley)

I'll discuss some aspects of the geometry of the Wasserstein space of probability measures, both at a formal level and a rigorous level : tangent cones, curvature and parallel transport.

Updated on Dec 02, 2013 02:49 PM PST
3. # MGR Programmatic Seminar: On the asymptotic behavior of global solutions of Einstein's equations.

Location: MSRI: Simons Auditorium
Speakers: Hans Lindblad (Johns Hopkins University)
Updated on Oct 30, 2013 09:12 AM PDT
4. # Converging Spaces Reading Seminar

Location: MSRI: Baker Board Room

This seminar is open to all faculty, postdocs and doctoral students involved in either program at MSRI in Fall 2013.  It is designed to bring the two programs together as both fields require an understanding of the convergence of manifolds and metric measure spaces.  We meet Wednesday afternoons 3-5pm in the Baker Boardroom.

Created on Dec 02, 2013 02:40 PM PST
5. # PD Seminar: Regularity of shadows and the singular set associated to a Monge-Ampere equation

Location: 740 Evans Hall
Speakers: Emanuel Indrei (Carnegie Mellon University)
Updated on Nov 15, 2013 09:42 AM PST
6. # PD Seminar: The spherically symmetric SU(2) Einstein-Yang-Mills equations

Location: 740 Evans Hall
Speakers: Daniel Jackson (Monash University)
Updated on Nov 15, 2013 09:41 AM PST
7. # MGR Programmatic Seminar: Some mathematical aspects of the Hawking effect for rotating black holes

Location: MSRI: Simons Auditorium
Speakers: Dietrich Hafner (Université de Grenoble I (Joseph Fourier))

The aim of this talk is to give a mathematically rigourous description of the Hawking effect for fermions in the setting of the collapse of a rotating charged star. We show that an observer who is located far away from the star and at rest with respect to the Boyer Lindquist coordinates observes the emergence of a thermal state when his proper time goes to infinity. We first introduce a model of the collapse of the star. We suppose that the spacetime outside the star is given by the Kerr-Newman metric. The assumptions on the asymptotic behavior of the surface of the star are inspired by the asymptotic behavior of certain timelike geodesics in the Kerr-Newman metric. The Dirac equation is then written using coordinates and a Newman-Penrose tetrad which are adapted to the collapse. This coordinate system and tetrad are based on the so called simple null geodesics. The quantization of Dirac fields in a globally hyperbolic space-time is described. We formulate and prove a theorem about the Hawking effect in this setting.

Updated on Nov 18, 2013 09:38 AM PST
8. # Converging Spaces Reading Seminar

Location: MSRI: Baker Board Room

This seminar is open to all faculty, postdocs and doctoral students involved in either program at MSRI in Fall 2013.  It is designed to bring the two programs together as both fields require an understanding of the convergence of manifolds and metric measure spaces.  We meet Wednesday afternoons 3-5pm in the Baker Boardroom.

Updated on Sep 12, 2013 09:37 AM PDT
9. # Geroch Lunch Seminar

Location: MSRI: Baker Board Room

The speaker will be chosen among the members of the audience at the time of the event. One or more volunteers from the audience will present a current topic of research, possibly but not necessarily one on which they are currently working.

Updated on Sep 16, 2013 02:56 PM PDT
10. # OT Programmatic Seminar: On kinetic models for the collective self-organization of agents.

Location: MSRI: Baker Board Room
Speakers: Konstantina Trivisa (University of Maryland)

A class of kinetic flocking. models is  presented for the collective self-organization of agents. Results  on the global existence of weak solutions as well as a  hydrodynamic limit will be discussed. The main tools employed in the analysis  are the velocity averaging lemma and the relative entropy method. This is joint work with T. Karper and A. Mellet.

Updated on Nov 27, 2013 11:31 AM PST
11. # OT Programmatic Seminar: Optimal transportation in sub-Riemannian geometry

Location: MSRI: Baker Board Room
Speakers: Ludovic Rifford (Université de Nice Sophia Antipolis)

We make a state of the art and raise several question about optimal transport problems in sub-Riemannian manifolds.

Updated on Nov 27, 2013 02:27 PM PST
12. # MGR Programmatic Seminar: Numerically evolving the Ricci Flow on S^3

Location: MSRI: Simons Auditorium
Speakers: Oscar Reula (Universidad Nacional de Cordoba)

In this talk I will discuss some attempts to evolve a Ricci Flows in S^3. I will focus in different types of problems that arise in this activity:

Some analytical ones, among them, which are the convenient gauge choices, which are the questions one would like to answer (hopping on getting some feedback from the audience), and the way to extract relevant global information from the numerical solution.

On the other hand, evolving numerically partial differential equations on manifolds with non-trivial topology implies the use of multiple grids, each one representing a coordinate patch, and the union of them, a chart for the underlying manifold. So numerical techniques to deal with these situations have to be properly implemented so that information from one of the grids can be carried to the others, and how to prevent spurious solutions to appear and dominate the evolution.

Updated on Nov 12, 2013 11:45 AM PST
13. # MSRI/Evans Lecture: Could the Universe have an Exotic Topology?

Location: UC Berkeley, 60 Evans Hall
Speakers: Vincent Moncrief (Yale University)

Astronomical observations have long been interpreted to support a so-called 'cosmological principle' according to which the universe, viewed on a sufficiently large, coarse-grained scale, is spatially homogeneous and isotropic. Up to an overall, time-dependent scale factor, only three Riemannian manifolds are compatible with this principle, namely the constant curvature spaces S3, E3 and H3 or spherical, flat and hyperbolic space-forms respectively and these provide the bases for the standard Friedmann, Robertson-Walker, Lemaîtra (FRWL) cosmological models. But astronomers only observe a fraction of the universe and the possibility remains open that its actual topology could be more 'exotic' and perhaps only locally compatible with isotropy and homogeniety. In this talk I shall discuss some mathematical evidence suggesting that the Einstein field equations, formulated on much more general manifolds than the FRWL ones listed above, contain a dynamical mechanism according to which the universe will, in the direction of cosmological expansion, be volume dominated by regions that are asymptotically homogeneous and isotropic.

Updated on Nov 25, 2013 01:05 PM PST
14. # Geroch Lunch Seminar

Location: MSRI: Baker Board Room

The speaker will be chosen among the members of the audience at the time of the event. One or more volunteers from the audience will present a current topic of research, possibly but not necessarily one on which they are currently working.

Updated on Sep 16, 2013 02:56 PM PDT
15. # OT Programmatic Seminar: Ricci curvature type lower bounds for sub-Riemannian structures on Sasakian manifolds

Location: MSRI: Baker Board Room
Speakers: Paul Woon Yin Lee (Chinese University of Hong Kong)

In this talk, we introduce a type of Ricci curvature lower bound for a natural sub-Riemannian structure on Sasakian manifolds and discuss various consequences under this condition.

Updated on Nov 13, 2013 02:49 PM PST
16. # MGR Programmatic Seminar: BKL singularity, spikes and inhomogeneous cosmology

Location: MSRI: Simons Auditorium
Speakers: Woei Chet Lim (University of Waikato)

How does a general solution to the EFE behave near a singularity? The BKL conjecture states that a generic singularity is vacuum-dominated, local and oscillatory. However, numerical exploration discovered non-local inhomogeneous structures called spikes, whose exact solutions are discovered in 2008. Spikes provide a way to generate matter inhomogeneity in the alternative paradigm of inhomogeneous cosmology. The electromagnetic spike solutions are discovered recently.

Updated on Nov 08, 2013 09:46 AM PST
17. # Chancellor's Lecture - Topics in Analysis: Hidden convexity in nonlinear PDES

Location: 51 Evans Hall, UC Berkeley
Speakers: Yann Brenier (École Polytechnique)

Outline: Several examples of hidden convexity in nonlinear PDEs will be addressed. Most of them are related to the theory of “optimal transportation”, which is the theme of one of the two MSRI programs this fall: see http://www.msri.org/programs/277.

1) Fully nonlinear elliptic equations: The canonical example is the reduction of the Monge-Ampere equation (a fully nonlinear elliptic PDE related to the “Minkowski problem” in geometry) to a convex minimization problem, a la Kantorovich, which can be solved by convex duality techniques. Connections with combinatorial optimization and “optimal transport” will be discussed.

2) Mathematical fluid mechanics:
i) Some solutions to the Euler equations can be obtained by using the least action principle (following V.I. Arnold’s geometric interpretation), leading to the problem of “optimal incompressible transport”; this problem has a hidden convex structure which provides existence, uniqueness and partial regularity for its solution.
ii) The hydrostatic and semi-geostrophic limits of the Euler and Navier-Stokes equations are examples of very singular limits that cannot be justified on standard linear functional spaces but can be addressed successfully on suitable convex functional cones.

3) Electromagnetism and magnetohydrodynamics:
i) The nonlinear theory of electromagnetism by Born and Infeld is described by a system of nonlinear conservation laws (which leads to the standard Maxwell equations for fields of low intensity), which has an interesting hidden structure, showing very easily its hyperbolic nature; the high field limit of the BI equations will be discussed and related to the “optimal transport of currents”.
ii) The magnetic relaxation equations proposed by Moffatt can be seen as a natural extension to divergence-free vector fields of the scalar heat equation (following the interpretation of Jordan-Kinderlehrer-Otto); they form a very degenerate parabolic systems of PDEs with a hidden convex structure that enables us to show the global existence of “dissipative solutions” (in the spirit of P.-L. Lions and Ambrosio-Gigli-Savar´e).

Created on Aug 26, 2013 03:35 PM PDT
18. # MSRI/Evans Lecture: Inverse mean curvature flow, black holes and quasi-local mass

Location: UC Berkeley, 60 Evans Hall
Speakers: Kristen Moore (Stanford University)

Inverse mean curvature flow is a parabolic geometric evolution equation that expands a hypersurface at a rate given by the reciprocal of the mean curvature. In recent years it has proven to be an effective tool in the study problems in general relativity. In this talk I will discuss the role of inverse mean curvature flow in the study of black hole horizons and quasi-local concepts of mass and energy, and outline it's connection to the Penrose Conjecture.

Updated on Nov 19, 2013 10:57 AM PST
19. # MGR Programmatic Seminar: Exploring the corner: linearised gravitational waves near space-like and null-infinity

Location: MSRI: Simons Auditorium
Speakers: Joerg Frauendiener (University of Otago)

The conformal compactification introduced by Penrose in the late 1960s provides an interesting approach towards the numerical simulation of global properties of space-times. The work by Friedrich has put Penrose’s approach onto a firm mathematical footing, giving wellposedness and stability results for several finite initial (boundary) value problems of the (generalized) conformal field equations. In this talk we will discuss the geometrical and analytical foundations of these ideas and we present preliminary results for the evolution of linearized gravitational fields i.e., the zero-rest-mass spin-2 fields on Minkowski space.

Updated on Oct 30, 2013 09:03 AM PDT
20. # Villani Postdoc/Graduate Student Optimal Transport Seminar: Properties of weak CD(K,N) spaces

Location: MSRI: Baker Board Room
Speakers: Tuo Wang (Vienna University of Technology)
Updated on Nov 27, 2013 02:29 PM PST
21. # Villani Postdoc/Graduate Student Optimal Transport Seminar: Stability of CD/RCD spaces

Location: MSRI: Baker Board Room
Speakers: Raquel Perales Aguilar (SUNY)
Updated on Nov 04, 2013 03:43 PM PST
22. # Chancellor's Lecture - Topics in Analysis: Hidden convexity in nonlinear PDES

Location: 51 Evans Hall, UC Berkeley
Speakers: Yann Brenier (École Polytechnique)

Outline: Several examples of hidden convexity in nonlinear PDEs will be addressed. Most of them are related to the theory of “optimal transportation”, which is the theme of one of the two MSRI programs this fall: see http://www.msri.org/programs/277.

1) Fully nonlinear elliptic equations: The canonical example is the reduction of the Monge-Ampere equation (a fully nonlinear elliptic PDE related to the “Minkowski problem” in geometry) to a convex minimization problem, a la Kantorovich, which can be solved by convex duality techniques. Connections with combinatorial optimization and “optimal transport” will be discussed.

2) Mathematical fluid mechanics:
i) Some solutions to the Euler equations can be obtained by using the least action principle (following V.I. Arnold’s geometric interpretation), leading to the problem of “optimal incompressible transport”; this problem has a hidden convex structure which provides existence, uniqueness and partial regularity for its solution.
ii) The hydrostatic and semi-geostrophic limits of the Euler and Navier-Stokes equations are examples of very singular limits that cannot be justified on standard linear functional spaces but can be addressed successfully on suitable convex functional cones.

3) Electromagnetism and magnetohydrodynamics:
i) The nonlinear theory of electromagnetism by Born and Infeld is described by a system of nonlinear conservation laws (which leads to the standard Maxwell equations for fields of low intensity), which has an interesting hidden structure, showing very easily its hyperbolic nature; the high field limit of the BI equations will be discussed and related to the “optimal transport of currents”.
ii) The magnetic relaxation equations proposed by Moffatt can be seen as a natural extension to divergence-free vector fields of the scalar heat equation (following the interpretation of Jordan-Kinderlehrer-Otto); they form a very degenerate parabolic systems of PDEs with a hidden convex structure that enables us to show the global existence of “dissipative solutions” (in the spirit of P.-L. Lions and Ambrosio-Gigli-Savar´e).

Created on Aug 26, 2013 03:32 PM PDT
23. # Converging Spaces Reading Seminar

Location: MSRI: Baker Board Room

This seminar is open to all faculty, postdocs and doctoral students involved in either program at MSRI in Fall 2013.  It is designed to bring the two programs together as both fields require an understanding of the convergence of manifolds and metric measure spaces.  We meet Wednesday afternoons 3-5pm in the Baker Boardroom.

Updated on Sep 12, 2013 09:36 AM PDT
24. # Villani Postdoc/Graduate Student Optimal Transport Seminar: Heat Equation

Location: MSRI: Baker Board Room
Speakers: Zahra Sinaei (École Polytechnique Fédérale de Lausanne (EPFL))
Created on Nov 04, 2013 04:04 PM PST
25. # OT Programmatic Seminar

Location: MSRI: Baker Board Room
Created on Oct 11, 2013 09:57 AM PDT
26. # OT Programmatic Seminar

Location: MSRI: Baker Board Room
Updated on Oct 10, 2013 04:41 PM PDT
27. # Chancellor's Lecture - Topics in Analysis: Hidden convexity in nonlinear PDES

Location: 51 Evans Hall, UC Berkeley
Speakers: Yann Brenier (École Polytechnique)

Outline: Several examples of hidden convexity in nonlinear PDEs will be addressed. Most of them are related to the theory of “optimal transportation”, which is the theme of one of the two MSRI programs this fall: see http://www.msri.org/programs/277.

1) Fully nonlinear elliptic equations: The canonical example is the reduction of the Monge-Ampere equation (a fully nonlinear elliptic PDE related to the “Minkowski problem” in geometry) to a convex minimization problem, a la Kantorovich, which can be solved by convex duality techniques. Connections with combinatorial optimization and “optimal transport” will be discussed.

2) Mathematical fluid mechanics:
i) Some solutions to the Euler equations can be obtained by using the least action principle (following V.I. Arnold’s geometric interpretation), leading to the problem of “optimal incompressible transport”; this problem has a hidden convex structure which provides existence, uniqueness and partial regularity for its solution.
ii) The hydrostatic and semi-geostrophic limits of the Euler and Navier-Stokes equations are examples of very singular limits that cannot be justified on standard linear functional spaces but can be addressed successfully on suitable convex functional cones.

3) Electromagnetism and magnetohydrodynamics:
i) The nonlinear theory of electromagnetism by Born and Infeld is described by a system of nonlinear conservation laws (which leads to the standard Maxwell equations for fields of low intensity), which has an interesting hidden structure, showing very easily its hyperbolic nature; the high field limit of the BI equations will be discussed and related to the “optimal transport of currents”.
ii) The magnetic relaxation equations proposed by Moffatt can be seen as a natural extension to divergence-free vector fields of the scalar heat equation (following the interpretation of Jordan-Kinderlehrer-Otto); they form a very degenerate parabolic systems of PDEs with a hidden convex structure that enables us to show the global existence of “dissipative solutions” (in the spirit of P.-L. Lions and Ambrosio-Gigli-Savar´e).

Created on Aug 26, 2013 03:28 PM PDT
28. # MSRI/Evans Lecture: On an information-theoretical interpolation inequality

Location: UC Berkeley, 60 Evans Hall
Speakers: Cedric Villani (Institute Henri Poincare)

In this talk I will review the history and use of an information-theoretical inequality introduced by Otto and I at the end of the nineties, which we called the HWI inequality; how it was used recently in some large-dimension results.

Updated on Oct 09, 2013 02:38 PM PDT
29. # Villani Postdoc/Graduate Student Optimal Transport Seminar: Properties of weak CD(K,N) spaces

Location: MSRI: Baker Board Room
Updated on Nov 04, 2013 03:41 PM PST
30. # PD Seminar: The geodesic hypothesis in general relativity

Location: 740 Evans Hall
Speakers: Shiwu Yang (University of Cambridge)
Updated on Nov 08, 2013 12:39 PM PST
31. # PD Seminar: Martingales, robust hedging and the Skorokhod embedding

Location: 740 Evans Hall
Speakers: Martin Huesmann (Universität Bonn)
Updated on Nov 07, 2013 10:24 AM PST
32. # Villani Postdoc/Graduate Student Optimal Transport Seminar: CD and CD*(K,N) spaces (including characterization)

Location: MSRI: Baker Board Room
Speakers: Christopher Policastro (University of California, Berkeley)
Updated on Nov 04, 2013 03:40 PM PST
33. # MGR Programmatic Seminar: Non-zero rest-mass fields in cyclic cosmologies.

Location: MSRI: Simons Auditorium
Speakers: Helmut Friedrich (Max-Planck-Institut fuer Gravitationsphysik)

It is shown that solutions to Einstein's field equations with positive cosmological constant can include non-zero rest-mass fields which coexist with and travel unimpeded across smooth conformal boundaries.

Updated on Nov 05, 2013 10:11 AM PST
34. # Chancellor's Lecture - Topics in Analysis: Hidden convexity in nonlinear PDES

Location: 51 Evans Hall, UC Berkeley
Speakers: Yann Brenier (École Polytechnique)

Outline: Several examples of hidden convexity in nonlinear PDEs will be addressed. Most of them are related to the theory of “optimal transportation”, which is the theme of one of the two MSRI programs this fall: see http://www.msri.org/programs/277.

1) Fully nonlinear elliptic equations: The canonical example is the reduction of the Monge-Ampere equation (a fully nonlinear elliptic PDE related to the “Minkowski problem” in geometry) to a convex minimization problem, a la Kantorovich, which can be solved by convex duality techniques. Connections with combinatorial optimization and “optimal transport” will be discussed.

2) Mathematical fluid mechanics:
i) Some solutions to the Euler equations can be obtained by using the least action principle (following V.I. Arnold’s geometric interpretation), leading to the problem of “optimal incompressible transport”; this problem has a hidden convex structure which provides existence, uniqueness and partial regularity for its solution.
ii) The hydrostatic and semi-geostrophic limits of the Euler and Navier-Stokes equations are examples of very singular limits that cannot be justified on standard linear functional spaces but can be addressed successfully on suitable convex functional cones.

3) Electromagnetism and magnetohydrodynamics:
i) The nonlinear theory of electromagnetism by Born and Infeld is described by a system of nonlinear conservation laws (which leads to the standard Maxwell equations for fields of low intensity), which has an interesting hidden structure, showing very easily its hyperbolic nature; the high field limit of the BI equations will be discussed and related to the “optimal transport of currents”.
ii) The magnetic relaxation equations proposed by Moffatt can be seen as a natural extension to divergence-free vector fields of the scalar heat equation (following the interpretation of Jordan-Kinderlehrer-Otto); they form a very degenerate parabolic systems of PDEs with a hidden convex structure that enables us to show the global existence of “dissipative solutions” (in the spirit of P.-L. Lions and Ambrosio-Gigli-Savar´e).

Created on Aug 26, 2013 03:25 PM PDT
35. # Converging Spaces Reading Seminar

Location: MSRI: Baker Board Room

This seminar is open to all faculty, postdocs and doctoral students involved in either program at MSRI in Fall 2013.  It is designed to bring the two programs together as both fields require an understanding of the convergence of manifolds and metric measure spaces.  We meet Wednesday afternoons 3-5pm in the Baker Boardroom.

Updated on Sep 12, 2013 09:36 AM PDT
36. # Geroch Lunch Seminar

Location: MSRI: Baker Board Room

The speaker will be chosen among the members of the audience at the time of the event. One or more volunteers from the audience will present a current topic of research, possibly but not necessarily one on which they are currently working.

Updated on Sep 16, 2013 02:55 PM PDT
37. # Villani Postdoc/Graduate Student Optimal Transport Seminar: Bochner formula

Location: MSRI: Baker Board Room
Speakers: Ling Xiao (Johns Hopkins University)
Updated on Nov 04, 2013 03:39 PM PST
38. # OT Programmatic Seminar: Arnold diffusion in nearly integrable Hamiltonian systems

Location: MSRI: Baker Board Room
Speakers: Chong-Qing Cheng (Nanjing University)

In this talk, I shall sketch the proof of Arnold diffsuion in nearly integrable Hamiltonian systems with three degrees of freedom $H(x,y)=h(y)+\epsilon P(x,y)$ where $(x,y)\in\mathbb{T}^3\times\mathbb{R}^3$. Under typical perturbation $\epsilon P$, the system admits connecting" orbit that passes through any two prescribed small balls in the same energy level $H^{-1}(E)$ provided $E$ is bigger than the minimum of the average action

Updated on Nov 06, 2013 09:31 AM PST
39. # MGR Programmatic Seminar: Numerical simulations of gravitational singularities

Location: MSRI: Simons Auditorium
Speakers: David Garfinkle (Oakland University)

The singularity theorems of Hawking, Penrose, and others predict that gravitational collapse results in spacetime singularities.

However, these theorems tell us very little about the nature of these singularities.  We can learn more by performing computer simulations of gravitational collapse and looking at the properties of the singularities that result.  The simulations can also give hints about what theorems might be proved about singularities.  This talk will review what has been learned from simulations and speculate about the prospects for future simulations and mathematical results.

Updated on Nov 05, 2013 10:27 AM PST
40. # Chancellor's Lecture - Topics in Analysis: Hidden convexity in nonlinear PDES

Location: 51 Evans Hall, UC Berkeley
Speakers: Yann Brenier (École Polytechnique)

Outline: Several examples of hidden convexity in nonlinear PDEs will be addressed. Most of them are related to the theory of “optimal transportation”, which is the theme of one of the two MSRI programs this fall: see http://www.msri.org/programs/277.

1) Fully nonlinear elliptic equations: The canonical example is the reduction of the Monge-Ampere equation (a fully nonlinear elliptic PDE related to the “Minkowski problem” in geometry) to a convex minimization problem, a la Kantorovich, which can be solved by convex duality techniques. Connections with combinatorial optimization and “optimal transport” will be discussed.

2) Mathematical fluid mechanics:
i) Some solutions to the Euler equations can be obtained by using the least action principle (following V.I. Arnold’s geometric interpretation), leading to the problem of “optimal incompressible transport”; this problem has a hidden convex structure which provides existence, uniqueness and partial regularity for its solution.
ii) The hydrostatic and semi-geostrophic limits of the Euler and Navier-Stokes equations are examples of very singular limits that cannot be justified on standard linear functional spaces but can be addressed successfully on suitable convex functional cones.

3) Electromagnetism and magnetohydrodynamics:
i) The nonlinear theory of electromagnetism by Born and Infeld is described by a system of nonlinear conservation laws (which leads to the standard Maxwell equations for fields of low intensity), which has an interesting hidden structure, showing very easily its hyperbolic nature; the high field limit of the BI equations will be discussed and related to the “optimal transport of currents”.
ii) The magnetic relaxation equations proposed by Moffatt can be seen as a natural extension to divergence-free vector fields of the scalar heat equation (following the interpretation of Jordan-Kinderlehrer-Otto); they form a very degenerate parabolic systems of PDEs with a hidden convex structure that enables us to show the global existence of “dissipative solutions” (in the spirit of P.-L. Lions and Ambrosio-Gigli-Savar´e).

Created on Aug 26, 2013 03:24 PM PDT
41. # Constraint FRG

Location: MSRI: Baker Board Room
Speakers: James Isenberg (University of Oregon)
Created on Nov 06, 2013 01:31 PM PST
42. # PD Seminar: The Einstein-Yang-Mills phase space and the First Law of black hole mechanics

Location: 740 Evans Hall
Speakers: Stephen McCormick (Monash University)
Updated on Oct 30, 2013 03:07 PM PDT
43. # PD Seminar: Adding a vanishing Dirichlet energy to the Monge cost: some surprising effects

Location: 740 Evans Hall
Speakers: Jean Louet (Université Paris-Sud (Orsay))
Updated on Oct 30, 2013 03:07 PM PDT
44. # Villani Postdoc/Graduate Student Optimal Transport Seminar: Comparison Theorems (Bishop-Gromov, Levy-Gromov, Caffarelli)

Location: MSRI: Simons Auditorium
Speakers: Jinxin Xue (University of Chicago)
Updated on Nov 04, 2013 03:39 PM PST
45. # OT Programmatic Seminar: The Cartan-Hadamard conjecture via optimal transport

Location: MSRI: Simons Auditorium
Speakers: Greg Kuperberg

Among all n-dimensional manifolds D with boundary, with some fixed volume, and with curvature bounded above by some constant κ, which one has the least surface area of its boundary? The nice answer that one might expect is a round ball with constant curvature κ.  In order to attain any positive lower bound on the surface area, we need extra assumptions concerning the topology and geometry of D.

The generalized Cartan-Hadamard conjecture is this isoperimetric inequality if D is a domain in a complete, simply connected manifold M with the same curvature bound κ and κ is non-positive.  This conjecture was proven by Weil and Bol in dimension 2, by Kleiner in dimension 3, and by Croke in dimension 4 when κ=0.

I will discuss a new interpretation of Croke's argument based on optimal transport and linear programming.  This interpretation allows a generalization, in dimensino 4, to positive κ and a partial generalization to negative κ.  This is joint work with Benoit Kloeckner.

Updated on Oct 31, 2013 09:49 AM PDT
46. # MGR Programmatic Seminar: Geometric Boundary Data for the Gravitational Field

Location: MSRI: Simons Auditorium
Speakers: Jeffrey Winicour (University of Pittsburgh)

An outstanding issue in the treatment of boundaries in general relativity has been the lack of a local geometric interpretation of the necessary boundary data. For the Cauchy problem, the initial data is supplied by the 3-metric and extrinsic curvature of the initial Cauchy hypersurface, subject to constraints. This Cauchy data determine a solution to Einstein's equations which is unique up to diffeomorphism.  I will describe how three pieces of unconstrained boundary data, which are associated locally with the geometry of the boundary, likewise determine a solution of the initial-boundary value problem which is unique, up to diffeomorphism. Two pieces of this data constitute a conformal class of rank-2 metrics, which represent the two gravitational degrees of freedom. The third piece, constructed from the extrinsic curvature of the boundary, determines the dynamical evolution of the boundary.

Updated on Oct 09, 2013 03:06 PM PDT
47. # Chancellor's Lecture - Topics in Analysis: Hidden convexity in nonlinear PDES

Location: 51 Evans Hall, UC Berkeley
Speakers: Yann Brenier (École Polytechnique)

Outline: Several examples of hidden convexity in nonlinear PDEs will be addressed. Most of them are related to the theory of “optimal transportation”, which is the theme of one of the two MSRI programs this fall: see http://www.msri.org/programs/277.

1) Fully nonlinear elliptic equations: The canonical example is the reduction of the Monge-Ampere equation (a fully nonlinear elliptic PDE related to the “Minkowski problem” in geometry) to a convex minimization problem, a la Kantorovich, which can be solved by convex duality techniques. Connections with combinatorial optimization and “optimal transport” will be discussed.

2) Mathematical fluid mechanics:
i) Some solutions to the Euler equations can be obtained by using the least action principle (following V.I. Arnold’s geometric interpretation), leading to the problem of “optimal incompressible transport”; this problem has a hidden convex structure which provides existence, uniqueness and partial regularity for its solution.
ii) The hydrostatic and semi-geostrophic limits of the Euler and Navier-Stokes equations are examples of very singular limits that cannot be justified on standard linear functional spaces but can be addressed successfully on suitable convex functional cones.

3) Electromagnetism and magnetohydrodynamics:
i) The nonlinear theory of electromagnetism by Born and Infeld is described by a system of nonlinear conservation laws (which leads to the standard Maxwell equations for fields of low intensity), which has an interesting hidden structure, showing very easily its hyperbolic nature; the high field limit of the BI equations will be discussed and related to the “optimal transport of currents”.
ii) The magnetic relaxation equations proposed by Moffatt can be seen as a natural extension to divergence-free vector fields of the scalar heat equation (following the interpretation of Jordan-Kinderlehrer-Otto); they form a very degenerate parabolic systems of PDEs with a hidden convex structure that enables us to show the global existence of “dissipative solutions” (in the spirit of P.-L. Lions and Ambrosio-Gigli-Savar´e).

Created on Aug 26, 2013 03:23 PM PDT
48. # Chern Lecture: Self-avoiding walk on the hexagonal lattice

Location: 50 Birge Hall, UC Berkeley
Speakers: Stanislav Smirnov

How many simple length $n$ trajectories one can draw on a lattice? It is easy to show that the number grows exponentially, but going beyond this observation is difficult. We will present our joint work with Hugo Duminil-Copin, giving a short and self-contained derivation of the Bernard Nienhuis conjecture that on hexagonal lattice this number grows like $(\sqrt{2+\sqrt{2}}^n$. Then we will discuss its relations to conformal invariance and other conjectured properties of the self-avoiding walk.

Updated on Oct 17, 2013 08:50 AM PDT
49. # Converging Spaces Reading Seminar

Location: MSRI: Simons Auditorium

This seminar is open to all faculty, postdocs and doctoral students involved in either program at MSRI in Fall 2013.  It is designed to bring the two programs together as both fields require an understanding of the convergence of manifolds and metric measure spaces.  We meet Wednesday afternoons 3-5pm in the Baker Boardroom.

Updated on Oct 18, 2013 10:43 AM PDT
50. # Geroch Lunch Seminar

Location: MSRI: Commons Room

The speaker will be chosen among the members of the audience at the time of the event. One or more volunteers from the audience will present a current topic of research, possibly but not necessarily one on which they are currently working.

Updated on Oct 22, 2013 03:03 PM PDT
51. # Villani Postdoc/Graduate Student Optimal Transport Seminar: Ricci curvature and displacement convexity; Brunn-Minkowski

Location: MSRI: Simons Auditorium
Speakers: Matthias Erbar (Rheinische Friedrich-Wilhelms-Universität Bonn)
Updated on Nov 04, 2013 03:38 PM PST
52. # Chern Lecture: CFT and SLE and 2D statistical physics

Location: 105 North Gate Hall, UC Berkeley
Speakers: Stanislav Smirnov

We will give an expository talk comparing two approaches to 2D lattice models of critical phenomena. Developed over two decades ago, Conformal Field Theory led to spectacular predictions for 2D lattice models:  e.g., critical percolation cluster a.s. has Hausdorff dimension 91/48.

While the algebraic framework of CFT is rather solid, rigorous arguments relating it to lattice models were lacking. More recently, a geometric approach involving random SLE curves was proposed by Oded Schramm, and developed by him, Greg Lawler, Wendelin Werner, Steffen Rohde and others. Not only this approach is completely rigorous, it  also constructs new objects of physical interest and gives results inaccessible by CFT means.

Updated on Oct 17, 2013 08:48 AM PDT
53. # MGR Programmatic Seminar: Nonlinear wave equations on time dependent inhomogeneous backgrounds.

Location: MSRI: Simons Auditorium
Speakers: Shiwu Yang (University of Cambridge)

We study the nonlinear wave equations on a class of asymptotically flat Lorentzian manifolds (R^{3+1}, g) with time dependent inhomogeneous metric g. Based on a new approach for proving the decay of solutions of linear wave equations, we give several applications to nonlinear problems. In particular, we show the small data global existence result for quasilinear wave equations satisfying the null condition on a class of time dependent inhomogeneous backgrounds which do not settle to any particular stationary metric.

Updated on Oct 09, 2013 02:59 PM PDT
54. # Chancellor's Lecture - Topics in Analysis: Hidden convexity in nonlinear PDES

Location: 51 Evans Hall, UC Berkeley
Speakers: Yann Brenier (École Polytechnique)

Outline: Several examples of hidden convexity in nonlinear PDEs will be addressed. Most of them are related to the theory of “optimal transportation”, which is the theme of one of the two MSRI programs this fall: see http://www.msri.org/programs/277.

1) Fully nonlinear elliptic equations: The canonical example is the reduction of the Monge-Ampere equation (a fully nonlinear elliptic PDE related to the “Minkowski problem” in geometry) to a convex minimization problem, a la Kantorovich, which can be solved by convex duality techniques. Connections with combinatorial optimization and “optimal transport” will be discussed.

2) Mathematical fluid mechanics:
i) Some solutions to the Euler equations can be obtained by using the least action principle (following V.I. Arnold’s geometric interpretation), leading to the problem of “optimal incompressible transport”; this problem has a hidden convex structure which provides existence, uniqueness and partial regularity for its solution.
ii) The hydrostatic and semi-geostrophic limits of the Euler and Navier-Stokes equations are examples of very singular limits that cannot be justified on standard linear functional spaces but can be addressed successfully on suitable convex functional cones.

3) Electromagnetism and magnetohydrodynamics:
i) The nonlinear theory of electromagnetism by Born and Infeld is described by a system of nonlinear conservation laws (which leads to the standard Maxwell equations for fields of low intensity), which has an interesting hidden structure, showing very easily its hyperbolic nature; the high field limit of the BI equations will be discussed and related to the “optimal transport of currents”.
ii) The magnetic relaxation equations proposed by Moffatt can be seen as a natural extension to divergence-free vector fields of the scalar heat equation (following the interpretation of Jordan-Kinderlehrer-Otto); they form a very degenerate parabolic systems of PDEs with a hidden convex structure that enables us to show the global existence of “dissipative solutions” (in the spirit of P.-L. Lions and Ambrosio-Gigli-Savar´e).

Created on Aug 26, 2013 03:22 PM PDT
55. # Chern Lecture: The Ising model of a ferromagnet from 1920 till 2020

Location: 50 Birge Hall, UC Berkeley
Speakers: Stanislav Smirnov

The Ising model is an archetypical model of order-disorder phase transition: though simple to formulate, it exhibits a complex behavior, much like the real-world phenomena in solid-state physics, ferromagnetism, chemistry, biology, computer science.  We will give a historical introduction, leading to more recent results about the 2D case, which allows a very detailed analysis.

Updated on Oct 17, 2013 08:48 AM PDT
56. # MSRI/Evans Lecture: A Compactness Theorem for Sequences of Rectifiable Metric Spaces

Location: UC Berkeley, 60 Evans Hall
Speakers: Christina Sormani (CUNY, Graduate Center)

A rectifiable metric space is a metric space (X,d) with a collection of bi-Lipschitz charts that cover all but a set of Hausdorff measure 0 of the space. Such a space can be endowed with an orientation and viewed as a rectifiable current space (X,d,T) where the T is called current structure and uses the charts to capture the notion of integration of forms (rigorously defined in work of Ambrosio-Kirchheim).  If the boundary of T, defined via Stoke's theorem, is also rectifiable, then (X,d,T) is called an integral current space.  This notion is defined in joint work with Stefan Wenger.

Riemannian manifolds of finite volume with cone singularities are examples of integral current spaces. If the manifold has a cusp singularity, the corresponding integral current space has the cusp removed. Here we will present the Tetrahedral Compactness Theorem which assumes certain uniform distance estimates on tetrahedra in a sequence of integral current spaces (or Riemannian manifolds) and a uniform upper bound on diameter and concludes that a subsequence converges in the Gromov-Hausdorff and Intrinsic Flat sense to an integral current space (in particular the limit is rectifiable and the same dimension as the sequence).

Updated on Oct 31, 2013 12:01 PM PDT
57. # Villani Postdoc/Graduate Student Optimal Transport Seminar: The HWI inequality

Location: MSRI: Baker Board Room
Updated on Nov 04, 2013 09:11 AM PST
58. # Chern Lectures

Location: University of California, Berkeley
Created on Jul 22, 2013 02:41 PM PDT
59. # PD Seminar: Convergence of harmonic maps.

Location: 740 Evans Hall
Speakers: Zahra Sinaei (École Polytechnique Fédérale de Lausanne (EPFL))
Updated on Oct 23, 2013 04:36 PM PDT
60. # PD Seminar: Rigidity of singularities and Lorentzian splitting geometry.

Location: 740 Evans Hall
Speakers: Carlos Vega (University of Miami)
Updated on Oct 23, 2013 04:35 PM PDT
61. # Monge and Kantorovich Meet Einstein

Location: MSRI: Simons Auditorium
Speakers: Robert McCann (University of Toronto)
Created on Nov 01, 2013 09:10 AM PDT
62. # MGR Programmatic Seminar: On construction of time functions.

Location: MSRI: Simons Auditorium
Speakers: Albert Fathi (École Normale Supérieure de Lyon)

This is a joint work with Antonio Siconolfi. The purpose of this lecture is to introduce a different way to obtain Lipschitz time functions on causal Lorentzian manifolds. We will show that they can be obtained from a kind of degenerate auxiliary Finsler metric. We will also explain how this leads to the existence of smooth time functions. A feature of this approach is that it works more generally for fields of cones on a manifold. Our approach evolved from our work on smooth sub-solutions of the Hamilton-Jacobi Equation and the relevance of the Aubry set to this problem. However no prior knowledge of this last subject will be used in the lecture.

Updated on Oct 11, 2013 10:33 AM PDT
63. # Chancellor's Lecture - Topics in Analysis: Hidden convexity in nonlinear PDES

Location: 51 Evans Hall, UC Berkeley
Speakers: Yann Brenier (École Polytechnique)

Outline: Several examples of hidden convexity in nonlinear PDEs will be addressed. Most of them are related to the theory of “optimal transportation”, which is the theme of one of the two MSRI programs this fall: see http://www.msri.org/programs/277.

1) Fully nonlinear elliptic equations: The canonical example is the reduction of the Monge-Ampere equation (a fully nonlinear elliptic PDE related to the “Minkowski problem” in geometry) to a convex minimization problem, a la Kantorovich, which can be solved by convex duality techniques. Connections with combinatorial optimization and “optimal transport” will be discussed.

2) Mathematical fluid mechanics:
i) Some solutions to the Euler equations can be obtained by using the least action principle (following V.I. Arnold’s geometric interpretation), leading to the problem of “optimal incompressible transport”; this problem has a hidden convex structure which provides existence, uniqueness and partial regularity for its solution.
ii) The hydrostatic and semi-geostrophic limits of the Euler and Navier-Stokes equations are examples of very singular limits that cannot be justified on standard linear functional spaces but can be addressed successfully on suitable convex functional cones.

3) Electromagnetism and magnetohydrodynamics:
i) The nonlinear theory of electromagnetism by Born and Infeld is described by a system of nonlinear conservation laws (which leads to the standard Maxwell equations for fields of low intensity), which has an interesting hidden structure, showing very easily its hyperbolic nature; the high field limit of the BI equations will be discussed and related to the “optimal transport of currents”.
ii) The magnetic relaxation equations proposed by Moffatt can be seen as a natural extension to divergence-free vector fields of the scalar heat equation (following the interpretation of Jordan-Kinderlehrer-Otto); they form a very degenerate parabolic systems of PDEs with a hidden convex structure that enables us to show the global existence of “dissipative solutions” (in the spirit of P.-L. Lions and Ambrosio-Gigli-Savar´e).

Created on Aug 26, 2013 03:12 PM PDT
64. # Converging Spaces Reading Seminar

Location: MSRI: Baker Board Room

This seminar is open to all faculty, postdocs and doctoral students involved in either program at MSRI in Fall 2013.  It is designed to bring the two programs together as both fields require an understanding of the convergence of manifolds and metric measure spaces.  We meet Wednesday afternoons 3-5pm in the Baker Boardroom.

Updated on Sep 12, 2013 09:35 AM PDT
65. # Geroch Lunch Seminar

Location: MSRI: Baker Board Room

The speaker will be chosen among the members of the audience at the time of the event. One or more volunteers from the audience will present a current topic of research, possibly but not necessarily one on which they are currently working.

Updated on Sep 16, 2013 02:54 PM PDT
66. # OT Programmatic Seminar: On Gluing Techniques in Calibrated Geometry

Location: MSRI: Baker Board Room
Speakers: yongsheng Zhang (Northeast (Dongbei) Normal University)

In this talk, we will discuss some gluing techniques in calibrated geometry. We prove that for a compact manifold, there exist lots of metrics in any conformal class, with respect to which, in each nonzero de Rham current homology class of dimension smaller than half the manifold dimension, an area minimizer can be realized by a liner combination of some fixed finitely many smooth submanifolds (viewed as currents).

We can also apply similar gluing techniques to a submanifold with mild singularities. For instance, we construct examples of compact Riemannian manifolds which support (coflatly) calibrated codimension-one singular compact submanifolds. If time permits, we may discuss some connections between semi-definite calibrated geometry and optimal transportations discovered in "Pseudo-Riemannian geometry calibrates optimal transportation" by Kim, McCann and Warren.

Updated on Oct 24, 2013 09:35 AM PDT
67. # OT Programmatic Seminar: Optimal Transport Problem For Contact Structures

Location: MSRI: Baker Board Room
Speakers: Fraydoun Rezakhanlou

In the Monge--Kantorovich transportation problem, we search for a plan that minimizes the cost of transporting mass from a set of locations  to another set of locations. According to a result of Moser, two volume forms on a compact Manifold of the same total volume are isomorphic and a solution to Monge--Kantorovich  problem offers a special solution to Moser's problem. A celebrated result of Gray asserts that if instead of volume forms we take two contact structures on a compact manifold, then they are isomorphic provided that they can be connected by a smooth arc of contact structures. In this talk, I discuss an optimal transport problem for Gray's result which has a similar flavour as Benamou-Brenier's formulation of  Monge--Kantorovich problem.

Updated on Oct 24, 2013 09:33 AM PDT
68. # MGR Programmatic Seminar: Future stability of cosmological models without cosmological constant

Location: MSRI: Simons Auditorium
Speakers: Ernesto-Miguel Nungesser Y Luengo (Trinity College)

There are several recent deep results concerning future stability of solutions to the Einstein-Vlasov and Einstein-Euler-system with a cosmological constant. In this talk we will present some results concerning the case of a vanishing cosmological constant and assuming that the spacetime is homogeneous. Recent results will be highlighted with an outlook of how they can be generalized.

Updated on Oct 08, 2013 12:24 PM PDT
69. # Chancellor's Lecture - Topics in Analysis: Hidden convexity in nonlinear PDES

Location: 51 Evans Hall, UC Berkeley
Speakers: Yann Brenier (École Polytechnique)

Outline: Several examples of hidden convexity in nonlinear PDEs will be addressed. Most of them are related to the theory of “optimal transportation”, which is the theme of one of the two MSRI programs this fall: see http://www.msri.org/programs/277.

1) Fully nonlinear elliptic equations: The canonical example is the reduction of the Monge-Ampere equation (a fully nonlinear elliptic PDE related to the “Minkowski problem” in geometry) to a convex minimization problem, a la Kantorovich, which can be solved by convex duality techniques. Connections with combinatorial optimization and “optimal transport” will be discussed.

2) Mathematical fluid mechanics:
i) Some solutions to the Euler equations can be obtained by using the least action principle (following V.I. Arnold’s geometric interpretation), leading to the problem of “optimal incompressible transport”; this problem has a hidden convex structure which provides existence, uniqueness and partial regularity for its solution.
ii) The hydrostatic and semi-geostrophic limits of the Euler and Navier-Stokes equations are examples of very singular limits that cannot be justified on standard linear functional spaces but can be addressed successfully on suitable convex functional cones.

3) Electromagnetism and magnetohydrodynamics:
i) The nonlinear theory of electromagnetism by Born and Infeld is described by a system of nonlinear conservation laws (which leads to the standard Maxwell equations for fields of low intensity), which has an interesting hidden structure, showing very easily its hyperbolic nature; the high field limit of the BI equations will be discussed and related to the “optimal transport of currents”.
ii) The magnetic relaxation equations proposed by Moffatt can be seen as a natural extension to divergence-free vector fields of the scalar heat equation (following the interpretation of Jordan-Kinderlehrer-Otto); they form a very degenerate parabolic systems of PDEs with a hidden convex structure that enables us to show the global existence of “dissipative solutions” (in the spirit of P.-L. Lions and Ambrosio-Gigli-Savar´e).

Created on Aug 26, 2013 03:11 PM PDT
70. # PD Seminar: Linear waves on Kerr--de Sitter cosmologies

Location: 740 Evans Hall
Speakers: Volker Schlue (University of Toronto)
Updated on Oct 17, 2013 11:27 AM PDT
71. # PD Seminar: Interior curvature estimates and the asymptotic Plateau problem in hyperbolic space

Location: 740 Evans Hall
Speakers: Ling Xiao (Johns Hopkins University)
Updated on Oct 17, 2013 11:26 AM PDT
72. # MGR Programmatic Seminar: On local wellposedness of ideal relativistic, and more general, fluids.

Location: MSRI: Simons Auditorium
Speakers: Robert Beig (Universität Wien)

We exhibit a class of theories, with the relativistic fluid a special case, which naturally take the form of a symmetric hyperbolic system. The 'reason' for this is that they possess a convex extension, with the role of convex entropy being played by the particle number density. This is joint work with Philippe LeFloch.

Updated on Oct 10, 2013 11:55 AM PDT
73. # Chancellor's Lecture - Topics in Analysis: Hidden convexity in nonlinear PDES

Location: 51 Evans Hall, UC Berkeley
Speakers: Yann Brenier (École Polytechnique)

Outline: Several examples of hidden convexity in nonlinear PDEs will be addressed. Most of them are related to the theory of “optimal transportation”, which is the theme of one of the two MSRI programs this fall: see http://www.msri.org/programs/277.

1) Fully nonlinear elliptic equations: The canonical example is the reduction of the Monge-Ampere equation (a fully nonlinear elliptic PDE related to the “Minkowski problem” in geometry) to a convex minimization problem, a la Kantorovich, which can be solved by convex duality techniques. Connections with combinatorial optimization and “optimal transport” will be discussed.

2) Mathematical fluid mechanics:
i) Some solutions to the Euler equations can be obtained by using the least action principle (following V.I. Arnold’s geometric interpretation), leading to the problem of “optimal incompressible transport”; this problem has a hidden convex structure which provides existence, uniqueness and partial regularity for its solution.
ii) The hydrostatic and semi-geostrophic limits of the Euler and Navier-Stokes equations are examples of very singular limits that cannot be justified on standard linear functional spaces but can be addressed successfully on suitable convex functional cones.

3) Electromagnetism and magnetohydrodynamics:
i) The nonlinear theory of electromagnetism by Born and Infeld is described by a system of nonlinear conservation laws (which leads to the standard Maxwell equations for fields of low intensity), which has an interesting hidden structure, showing very easily its hyperbolic nature; the high field limit of the BI equations will be discussed and related to the “optimal transport of currents”.
ii) The magnetic relaxation equations proposed by Moffatt can be seen as a natural extension to divergence-free vector fields of the scalar heat equation (following the interpretation of Jordan-Kinderlehrer-Otto); they form a very degenerate parabolic systems of PDEs with a hidden convex structure that enables us to show the global existence of “dissipative solutions” (in the spirit of P.-L. Lions and Ambrosio-Gigli-Savar´e).

Created on Aug 26, 2013 03:10 PM PDT
74. # Converging Spaces Reading Seminar

Location: MSRI: Baker Board Room

This seminar is open to all faculty, postdocs and doctoral students involved in either program at MSRI in Fall 2013.  It is designed to bring the two programs together as both fields require an understanding of the convergence of manifolds and metric measure spaces.  We meet Wednesday afternoons 3-5pm in the Baker Boardroom.

Updated on Sep 12, 2013 09:34 AM PDT
75. # Geroch Lunch Seminar

Location: MSRI: Baker Board Room

The speaker will be chosen among the members of the audience at the time of the event. One or more volunteers from the audience will present a current topic of research, possibly but not necessarily one on which they are currently working.

Updated on Sep 16, 2013 02:54 PM PDT
76. # OT Programmatic Seminar: Sub-level Set Convex Analysis

Location: MSRI: Baker Board Room
Speakers: Robert Jensen (Loyola University)

Upper semi-continuous functions which have sub-level convex sets are close cousins to and contain the convex functions.  Such functions are also called quasi-convex (e.g., http://en.wikipedia.org/wiki/Quasiconvex_function), but this term also can refer to functions which give rise to functionals that are weakly lower semi-continuous.  In this talk I will investigate the connection between sub-level set convex functions and a nonlinear, degenerate elliptic PDE.  I will describe properties of solutions of this PDE, including existence, uniqueness, and regularity.  The context for this work is in the Crandall-Lions theory of viscosity solutions.

Updated on Oct 15, 2013 10:52 AM PDT
77. # OT Programmatic Seminar: Stable stationary states for repulsive-attractive potentials

Location: MSRI: Baker Board Room
Speakers: Jose Carrillo (Imperial College, London)

In this talk we consider local minimizers (in the topology of transport distances) of the interaction energy associated to a repulsive-attractive potential. We show how the dimensionality of the support of local minimizers is related to the repulsive strength of the potential at the origin. This is related to pattern formation in some simple models of collective behavior.

Updated on Oct 15, 2013 10:51 AM PDT
78. # MGR Programmatic Seminar: Resonances in general relativity

Location: MSRI: Simons Auditorium
Speakers: Semyon Dyatlov (Massachusetts Institute of Technology)

We discuss long time behavior of linear scalar waves on Kerr and Kerr-de Sitter black hole backgrounds and their stationary perturbations. The physical motivation comes from the analysis of gravitational waves emitted during the ringdown stage of a large scale event (such as merging with another black hole). The properties of these waves, and their frequencies, called quasi-normal modes or resonances, depend on the structure of the set of all trapped light rays.

In the considered Kerr(-de Sitter) case, the trapped set is r-normally hyperbolic and we can provide a detailed description of quasi-normal modes and long-time behavior of linear waves.

Updated on Sep 19, 2013 01:14 PM PDT
79. # Chancellor's Lecture - Topics in Analysis: Hidden convexity in nonlinear PDES

Location: 51 Evans Hall, UC Berkeley
Speakers: Yann Brenier (École Polytechnique)

Outline: Several examples of hidden convexity in nonlinear PDEs will be addressed. Most of them are related to the theory of “optimal transportation”, which is the theme of one of the two MSRI programs this fall: see http://www.msri.org/programs/277.

1) Fully nonlinear elliptic equations: The canonical example is the reduction of the Monge-Ampere equation (a fully nonlinear elliptic PDE related to the “Minkowski problem” in geometry) to a convex minimization problem, a la Kantorovich, which can be solved by convex duality techniques. Connections with combinatorial optimization and “optimal transport” will be discussed.

2) Mathematical fluid mechanics:
i) Some solutions to the Euler equations can be obtained by using the least action principle (following V.I. Arnold’s geometric interpretation), leading to the problem of “optimal incompressible transport”; this problem has a hidden convex structure which provides existence, uniqueness and partial regularity for its solution.
ii) The hydrostatic and semi-geostrophic limits of the Euler and Navier-Stokes equations are examples of very singular limits that cannot be justified on standard linear functional spaces but can be addressed successfully on suitable convex functional cones.

3) Electromagnetism and magnetohydrodynamics:
i) The nonlinear theory of electromagnetism by Born and Infeld is described by a system of nonlinear conservation laws (which leads to the standard Maxwell equations for fields of low intensity), which has an interesting hidden structure, showing very easily its hyperbolic nature; the high field limit of the BI equations will be discussed and related to the “optimal transport of currents”.
ii) The magnetic relaxation equations proposed by Moffatt can be seen as a natural extension to divergence-free vector fields of the scalar heat equation (following the interpretation of Jordan-Kinderlehrer-Otto); they form a very degenerate parabolic systems of PDEs with a hidden convex structure that enables us to show the global existence of “dissipative solutions” (in the spirit of P.-L. Lions and Ambrosio-Gigli-Savar´e).

Created on Aug 26, 2013 03:09 PM PDT
80. # Villani Postdoc/Graduate Student Optimal Transport Seminar

Location: MSRI: Baker Board Room
Updated on Sep 13, 2013 10:36 AM PDT
81. # MSRI/Evans Lecture: Polyconvex integrands in the calculus of variations.

Location: UC Berkeley, 60 Evans Hall
Speakers: Wilfrid Gangbo (Georgia Institute of Technology)

Abstract

Updated on Oct 16, 2013 03:43 PM PDT
82. # Villani Postdoc/Graduate Student Optimal Transport Seminar

Location: MSRI: Baker Board Room
Updated on Sep 13, 2013 10:36 AM PDT
83. # MGR Programmatic Seminar: Local well-posedness for the minimal surface equation in Minkowski space

Location: MSRI: Baker Board Room
Speakers: Boris Ettinger (Princeton University)

The minimal surface equation for timelike surfaces of the Minkowski space is a quasi-linear wave equation. The nonlinear part of the equation exhibits a cancellation known as the null condition. We replicate the strategy of Smith and Tataru of constructing a wave-packet parametrix, which coupled with a space-time estimates for the null form allows us to lower the regularity compared to the general result for the quasilinear wave equation obtained by Smith and Tataru.

Updated on Oct 11, 2013 10:31 AM PDT
84. # Converging Spaces Reading Seminar

Location: MSRI: Baker Board Room

This seminar is open to all faculty, postdocs and doctoral students involved in either program at MSRI in Fall 2013.  It is designed to bring the two programs together as both fields require an understanding of the convergence of manifolds and metric measure spaces.  We meet Wednesday afternoons 3-5pm in the Baker Boardroom.

Updated on Sep 12, 2013 09:34 AM PDT
85. # Geroch Lunch Seminar

Location: MSRI: Baker Board Room

The speaker will be chosen among the members of the audience at the time of the event. One or more volunteers from the audience will present a current topic of research, possibly but not necessarily one on which they are currently working.

Updated on Sep 16, 2013 02:53 PM PDT
86. # MGR Programmatic Seminar: The angular momentum-mass inequality for general axisymmetric initial data

Location: MSRI: Baker Board Room
Speakers: Marcus Khuri (SUNY)

Consider axisymmetric initial data for the Einstein equations, satisfying the dominant energy condition, and having two ends, one asymptotically flat and the other either asymptotically flat or asymptotically cylindrical.

Heuristic physical arguments lead to the following inequality mâ¥â|J| relating the total mass and angular momentum. Equality should be achieved if and only if the data arise from the exrteme Kerr spacetime. Dain established this inequality (along with the corresponding rigidity statement) when the data are maximal and vacuum, and subsequently several authors have improved upon and extended these results. Here we consider the general non-maximal case in which the matter fields satisfy the dominant energy condition, and introduce a natural deformation back to the maximal case which preserves all the relevant geometry. This procedure may then be used to establish the angular momentum-mass inequality (and rigidity

statement) in the general case, assuming that a solution exists to a canonical system of two elliptic equations. This is joint work with Ye Sle Cha.

Updated on Oct 11, 2013 10:31 AM PDT
87. # PD Seminar: Strict convexity properties of solutions to Monge-Ampere type equations

Location: 740 Evans Hall
Updated on Oct 10, 2013 12:57 PM PDT
88. # PD Seminar: Far from constant mean curvature solutions to the Einstein constraint equations on compact manifolds

Location: 740 Evans Hall
Updated on Oct 03, 2013 11:19 AM PDT

Location: MSRI: Simons Auditorium
Speakers: Max Fathi (Universite Paris VI)
Updated on Oct 09, 2013 10:21 AM PDT
90. # MGR Programmatic Seminar: Far-from CMC solutions to the Einstein Constraint Equations on Compact Manifolds with Boundary

Location: MSRI: Simons Auditorium
Speakers: Michael Holst (University of California)

In this talk we consider the conformal formulation of the Einstein constraint equations on a compact manifold M with boundary dM.

Under certain assumptions on the data, we show that near- and far-from-constant mean curvature solutions to the conformal formulation exist when a class of Robin boundary conditions commonly used in the literature for modeling black holes are imposed on dM.

This work is a natural extension of the work done recently by Holst and Tsogtgerel (2013), Holst, Nagy, and Tsogtgerel (2008), Maxwell (2004, 2005), and Dain (2004). Dain and Maxwell addressed initial data engineering for space-times that evolve to contain black holes, determining solutions to the conformal formulation on an asymptotically Euclidean manifold in the constant mean curvature (CMC) setting, with interior boundary conditions representing excised interior black hole regions.

Updated on Oct 02, 2013 01:30 PM PDT
91. # Chancellor's Lecture - Topics in Analysis: Hidden convexity in nonlinear PDES

Location: 51 Evans Hall, UC Berkeley
Speakers: Yann Brenier (École Polytechnique)

Outline: Several examples of hidden convexity in nonlinear PDEs will be addressed. Most of them are related to the theory of “optimal transportation”, which is the theme of one of the two MSRI programs this fall: see http://www.msri.org/programs/277.

1) Fully nonlinear elliptic equations: The canonical example is the reduction of the Monge-Ampere equation (a fully nonlinear elliptic PDE related to the “Minkowski problem” in geometry) to a convex minimization problem, a la Kantorovich, which can be solved by convex duality techniques. Connections with combinatorial optimization and “optimal transport” will be discussed.

2) Mathematical fluid mechanics:
i) Some solutions to the Euler equations can be obtained by using the least action principle (following V.I. Arnold’s geometric interpretation), leading to the problem of “optimal incompressible transport”; this problem has a hidden convex structure which provides existence, uniqueness and partial regularity for its solution.
ii) The hydrostatic and semi-geostrophic limits of the Euler and Navier-Stokes equations are examples of very singular limits that cannot be justified on standard linear functional spaces but can be addressed successfully on suitable convex functional cones.

3) Electromagnetism and magnetohydrodynamics:
i) The nonlinear theory of electromagnetism by Born and Infeld is described by a system of nonlinear conservation laws (which leads to the standard Maxwell equations for fields of low intensity), which has an interesting hidden structure, showing very easily its hyperbolic nature; the high field limit of the BI equations will be discussed and related to the “optimal transport of currents”.
ii) The magnetic relaxation equations proposed by Moffatt can be seen as a natural extension to divergence-free vector fields of the scalar heat equation (following the interpretation of Jordan-Kinderlehrer-Otto); they form a very degenerate parabolic systems of PDEs with a hidden convex structure that enables us to show the global existence of “dissipative solutions” (in the spirit of P.-L. Lions and Ambrosio-Gigli-Savar´e).

Created on Aug 26, 2013 03:03 PM PDT
92. # Converging Spaces Reading Seminar

Location: MSRI: Baker Board Room

This seminar is open to all faculty, postdocs and doctoral students involved in either program at MSRI in Fall 2013.  It is designed to bring the two programs together as both fields require an understanding of the convergence of manifolds and metric measure spaces.  We meet Wednesday afternoons 3-5pm in the Baker Boardroom.

Updated on Sep 12, 2013 09:33 AM PDT
93. # Geroch Lunch Seminar

Location: MSRI: Baker Board Room

The speaker will be chosen among the members of the audience at the time of the event. One or more volunteers from the audience will present a current topic of research, possibly but not necessarily one on which they are currently working.

Updated on Sep 16, 2013 02:53 PM PDT
94. # OT Programmatic Seminar: Symmetric Monge-Kantorovich problems and polar decompositions of vector fields

Location: MSRI: Simons Auditorium
Speakers: Nassif Ghoussoub (University of British Columbia)

For any given integer N larger than 2, we show that every bounded measurable vector field on a bounded domain in Euclidean space is N-cyclically monotone up to a measure preserving N-involution. The proof involves the solution of a multidimensional symmetric Monge-Kantorovich problem, which we first study in the case of a general cost function. The proof exploits a remarkable duality between measure preserving transformations that are N-involutions and Hamiltonian functions that are N-cyclically antisymmetric.

Updated on Sep 26, 2013 09:01 AM PDT
95. # MGR Programmatic Seminar: Symmetres and conserved quantities

Location: MSRI: Simons Auditorium
Speakers: Lars Andersson (Albert Einstein Institute)

In this talk, I will discuss the relation between Killing spinors, symmetry operators and conserved quantities. For the case of Maxwell test fields on the Kerr spacetime, the Killing spinor can be used to construct conserved currents not related to Noether currents, as well as higher order conserved tensors.

Updated on Sep 09, 2013 09:48 AM PDT
96. # Chancellor's Lecture - Topics in Analysis: Hidden convexity in nonlinear PDES

Location: 51 Evans Hall, UC Berkeley
Speakers: Yann Brenier (École Polytechnique)

Outline: Several examples of hidden convexity in nonlinear PDEs will be addressed. Most of them are related to the theory of “optimal transportation”, which is the theme of one of the two MSRI programs this fall: see http://www.msri.org/programs/277.

1) Fully nonlinear elliptic equations: The canonical example is the reduction of the Monge-Ampere equation (a fully nonlinear elliptic PDE related to the “Minkowski problem” in geometry) to a convex minimization problem, a la Kantorovich, which can be solved by convex duality techniques. Connections with combinatorial optimization and “optimal transport” will be discussed.

2) Mathematical fluid mechanics:
i) Some solutions to the Euler equations can be obtained by using the least action principle (following V.I. Arnold’s geometric interpretation), leading to the problem of “optimal incompressible transport”; this problem has a hidden convex structure which provides existence, uniqueness and partial regularity for its solution.
ii) The hydrostatic and semi-geostrophic limits of the Euler and Navier-Stokes equations are examples of very singular limits that cannot be justified on standard linear functional spaces but can be addressed successfully on suitable convex functional cones.

3) Electromagnetism and magnetohydrodynamics:
i) The nonlinear theory of electromagnetism by Born and Infeld is described by a system of nonlinear conservation laws (which leads to the standard Maxwell equations for fields of low intensity), which has an interesting hidden structure, showing very easily its hyperbolic nature; the high field limit of the BI equations will be discussed and related to the “optimal transport of currents”.
ii) The magnetic relaxation equations proposed by Moffatt can be seen as a natural extension to divergence-free vector fields of the scalar heat equation (following the interpretation of Jordan-Kinderlehrer-Otto); they form a very degenerate parabolic systems of PDEs with a hidden convex structure that enables us to show the global existence of “dissipative solutions” (in the spirit of P.-L. Lions and Ambrosio-Gigli-Savar´e).

Created on Aug 26, 2013 03:02 PM PDT
97. # PD Seminar: Type-II singularities for Ricci flow on $R^n$

Location: 740 Evans Hall
Speakers: Haotian Wu (MSRI - Mathematical Sciences Research Institute)
Updated on Sep 26, 2013 02:39 PM PDT
98. # PD Seminar: Noncollision singularities in the Newtonian N-body problem

Location: 740 Evans Hall
Speakers: Jinxin Xue (University of Chicago)
Updated on Sep 26, 2013 02:38 PM PDT
99. # MGR Programmatic Seminar: Stable big bang formation in near-flrw solutions to the einstein-scalar field system.

Location: MSRI: Simons Auditorium
Speakers: Jared Speck

I will discuss some results that I recently obtained in collaboration with Igor Rodnianski. Our main result is a proof of stable Big Bang formation in small perturbations of the well-known Friedmann-Lema^tre-Robertson-Walker (FLRW) solution to the Einstein-scalar eld system. To study near-FLRW solutions, we place data on a Cauchy hypersurface 1 that are close to the FLRW data (at time 1) as measured by a Sobolev norm. We then study the global behavior of the perturbed solution in the collapsing direction. We rst show that the spacetime region of interest can be foliated by a family of spacelike Cauchy hypersurfaces t; t 2 (0; 1]; of constant mean curva- ture  1 3 t 1: We then analyze the behavior of the solution as t # 0 and provide a detailed description of its asymptotics. Our main conclusion is that the perturbed solution remains globally close to the FLRW solution and has approximately monotonic behavior. In particular, the perturbed solution has a Big Bang singularity at 0: More precisely, as t # 0; various curvature invariants uniformly blow-up and the volume of t collapses to 0: These blow-up results demonstrate the validity of Penrose's Strong Cosmic Censorship conjecture for the past half of the perturbed spacetimes. We have also shown that the same results hold for the sti uid matter model.

From the point of view of analysis, our main results can be viewed as a proof of stable blow-up for an open set of solutions to a highly nonlinear elliptic-hyperbolic system. The most important aspect of our analysis is our identification of a new L2 type energy almost-monotonicity inequality that holds for the solutions under consideration. I will discuss, in particular, two aspects of our proof that are connected to the approximate monotonicity and that may be of general interest: i) I will exhibit two gauges in which the approximate monotonicity is visible: constant mean curvature-transported spatial coordinates gauge, and a closely related one-parameter family of gauges involving well-chosen parabolic PDEs for the lapse function; ii) I will show how to derive L2 type energy estimates for
solutions to the Einstein equations directly in transported spatial coordinates.

Updated on Oct 03, 2013 10:11 AM PDT
100. # Chancellor's Lecture - Topics in Analysis: Hidden convexity in nonlinear PDES

Location: 51 Evans Hall, UC Berkeley
Speakers: Yann Brenier (École Polytechnique)

Outline: Several examples of hidden convexity in nonlinear PDEs will be addressed. Most of them are related to the theory of “optimal transportation”, which is the theme of one of the two MSRI programs this fall: see http://www.msri.org/programs/277.

1) Fully nonlinear elliptic equations: The canonical example is the reduction of the Monge-Ampere equation (a fully nonlinear elliptic PDE related to the “Minkowski problem” in geometry) to a convex minimization problem, a la Kantorovich, which can be solved by convex duality techniques. Connections with combinatorial optimization and “optimal transport” will be discussed.

2) Mathematical fluid mechanics:
i) Some solutions to the Euler equations can be obtained by using the least action principle (following V.I. Arnold’s geometric interpretation), leading to the problem of “optimal incompressible transport”; this problem has a hidden convex structure which provides existence, uniqueness and partial regularity for its solution.
ii) The hydrostatic and semi-geostrophic limits of the Euler and Navier-Stokes equations are examples of very singular limits that cannot be justified on standard linear functional spaces but can be addressed successfully on suitable convex functional cones.

3) Electromagnetism and magnetohydrodynamics:
i) The nonlinear theory of electromagnetism by Born and Infeld is described by a system of nonlinear conservation laws (which leads to the standard Maxwell equations for fields of low intensity), which has an interesting hidden structure, showing very easily its hyperbolic nature; the high field limit of the BI equations will be discussed and related to the “optimal transport of currents”.
ii) The magnetic relaxation equations proposed by Moffatt can be seen as a natural extension to divergence-free vector fields of the scalar heat equation (following the interpretation of Jordan-Kinderlehrer-Otto); they form a very degenerate parabolic systems of PDEs with a hidden convex structure that enables us to show the global existence of “dissipative solutions” (in the spirit of P.-L. Lions and Ambrosio-Gigli-Savar´e).

Created on Aug 26, 2013 02:59 PM PDT
101. # Converging Spaces Reading Seminar

Location: MSRI: Baker Board Room

This seminar is open to all faculty, postdocs and doctoral students involved in either program at MSRI in Fall 2013.  It is designed to bring the two programs together as both fields require an understanding of the convergence of manifolds and metric measure spaces.  We meet Wednesday afternoons 3-5pm in the Baker Boardroom.

Updated on Sep 12, 2013 09:32 AM PDT
102. # Geroch Lunch Seminar

Location: MSRI: Baker Board Room

The speaker will be chosen among the members of the audience at the time of the event. One or more volunteers from the audience will present a current topic of research, possibly but not necessarily one on which they are currently working.

Updated on Sep 16, 2013 02:52 PM PDT
103. # OT Programmatic Seminar: PDEs of Monge-Ampere type.

Location: MSRI: Simons Auditorium
Speakers: Neil Trudinger (Australian National University)

A considerable amount of research activity in recent years has been devoted to the study of nonlinear partial differential equations of Monge-Ampere type (MATEs) in connection with their applications to conformal geometry, optimal transportation and geometric optics. In this talk we plan to skim through a potpouri of recent results pertaining to  the underlying structural condition for regularity originating in a paper in 2005 by Ma, Wang and myself.

Updated on Sep 26, 2013 09:00 AM PDT
104. # MGR Programmatic Seminar: Unique continuation from infinity for linear waves.

Location: MSRI: Simons Auditorium
Speakers: Volker Schlue (University of Toronto)

We consider the problem of unique continuation from infinity for linear waves on a curved background. We derive new Carleman estimates from infinity for wave operators on Minkowski, Schwarzschild and certain perturbations thereof, which allow us to conclude that solutions to a wave equation vanishing to infinite order on suitable portions of future and past null infinity imply that the solution itself vanishes in an open region of spacetime. Surprisingly, the result in Schwarzschild is stronger than the one in Minkowski spacetime. Moreover, we show that our results are sharp (in particular infinite order vanishing is necessary). These results are motivated by questions in General Relativity. This is joint work with Spyros Alexakis and Arick Shao.

Updated on Aug 29, 2013 12:00 PM PDT
105. # Chancellor's Lecture - Topics in Analysis: Hidden convexity in nonlinear PDES

Location: 51 Evans Hall, UC Berkeley
Speakers: Yann Brenier (École Polytechnique)

Outline: Several examples of hidden convexity in nonlinear PDEs will be addressed. Most of them are related to the theory of “optimal transportation”, which is the theme of one of the two MSRI programs this fall: see http://www.msri.org/programs/277.

1) Fully nonlinear elliptic equations: The canonical example is the reduction of the Monge-Ampere equation (a fully nonlinear elliptic PDE related to the “Minkowski problem” in geometry) to a convex minimization problem, a la Kantorovich, which can be solved by convex duality techniques. Connections with combinatorial optimization and “optimal transport” will be discussed.

2) Mathematical fluid mechanics:
i) Some solutions to the Euler equations can be obtained by using the least action principle (following V.I. Arnold’s geometric interpretation), leading to the problem of “optimal incompressible transport”; this problem has a hidden convex structure which provides existence, uniqueness and partial regularity for its solution.
ii) The hydrostatic and semi-geostrophic limits of the Euler and Navier-Stokes equations are examples of very singular limits that cannot be justified on standard linear functional spaces but can be addressed successfully on suitable convex functional cones.

3) Electromagnetism and magnetohydrodynamics:
i) The nonlinear theory of electromagnetism by Born and Infeld is described by a system of nonlinear conservation laws (which leads to the standard Maxwell equations for fields of low intensity), which has an interesting hidden structure, showing very easily its hyperbolic nature; the high field limit of the BI equations will be discussed and related to the “optimal transport of currents”.
ii) The magnetic relaxation equations proposed by Moffatt can be seen as a natural extension to divergence-free vector fields of the scalar heat equation (following the interpretation of Jordan-Kinderlehrer-Otto); they form a very degenerate parabolic systems of PDEs with a hidden convex structure that enables us to show the global existence of “dissipative solutions” (in the spirit of P.-L. Lions and Ambrosio-Gigli-Savar´e).

Created on Aug 26, 2013 02:59 PM PDT
106. # PD Seminar: Bochner inequality and the entropic curvature dimension condition for metric measure spaces.

Location: 740 Evans Hall
Speakers: Matthias Erbar (Rheinische Friedrich-Wilhelms-Universität Bonn)
Updated on Sep 26, 2013 09:02 AM PDT
107. # PD Seminar: Microlocal analysis of radial points.

Location: 740 Evans Hall
Speakers: Nick Haber (Stanford University)
Updated on Sep 26, 2013 09:02 AM PDT
108. # OT Programmatic Seminar: On optimal transport and rotation numbers

Location: MSRI: Simons Auditorium
Speakers: Gershon Wolansky (Technion---Israel Institute of Technology)

I'll review optimal transport from a dynamical point of view, and consider some elementary examples of periodic orbits of probability measures on the circle, The definition of a rotation number for such orbits seems to be a natural object in this setting. I'll also consider minimal transport plans subjected to a prescribed rotation number.

Updated on Sep 19, 2013 10:34 AM PDT
109. # MGR Programmatic Seminar: On the existence, structure and stability of static and stationary solutions of the Einstein-Vlasov system

Location: MSRI: Simons Auditorium
Speakers: Hakan Andreasson (Chalmers University of Technology/University of Göteborg)

I will review the present status on the existence, structure and stability of static and stationary solutions of the Einstein-Vlasov system. Both analytical and numerical results will be discussed.

Updated on Aug 28, 2013 03:33 PM PDT
110. # Chancellor's Lecture - Topics in Analysis: Hidden convexity in nonlinear PDES

Location: 51 Evans Hall, UC Berkeley
Speakers: Yann Brenier (École Polytechnique)

Outline: Several examples of hidden convexity in nonlinear PDEs will be addressed. Most of them are related to the theory of “optimal transportation”, which is the theme of one of the two MSRI programs this fall: see http://www.msri.org/programs/277.

1) Fully nonlinear elliptic equations: The canonical example is the reduction of the Monge-Ampere equation (a fully nonlinear elliptic PDE related to the “Minkowski problem” in geometry) to a convex minimization problem, a la Kantorovich, which can be solved by convex duality techniques. Connections with combinatorial optimization and “optimal transport” will be discussed.

2) Mathematical fluid mechanics:
i) Some solutions to the Euler equations can be obtained by using the least action principle (following V.I. Arnold’s geometric interpretation), leading to the problem of “optimal incompressible transport”; this problem has a hidden convex structure which provides existence, uniqueness and partial regularity for its solution.
ii) The hydrostatic and semi-geostrophic limits of the Euler and Navier-Stokes equations are examples of very singular limits that cannot be justified on standard linear functional spaces but can be addressed successfully on suitable convex functional cones.

3) Electromagnetism and magnetohydrodynamics:
i) The nonlinear theory of electromagnetism by Born and Infeld is described by a system of nonlinear conservation laws (which leads to the standard Maxwell equations for fields of low intensity), which has an interesting hidden structure, showing very easily its hyperbolic nature; the high field limit of the BI equations will be discussed and related to the “optimal transport of currents”.
ii) The magnetic relaxation equations proposed by Moffatt can be seen as a natural extension to divergence-free vector fields of the scalar heat equation (following the interpretation of Jordan-Kinderlehrer-Otto); they form a very degenerate parabolic systems of PDEs with a hidden convex structure that enables us to show the global existence of “dissipative solutions” (in the spirit of P.-L. Lions and Ambrosio-Gigli-Savar´e).

Created on Aug 26, 2013 02:45 PM PDT
111. # Converging Spaces Reading Seminar

Location: MSRI: Baker Board Room

This seminar is open to all faculty, postdocs and doctoral students involved in either program at MSRI in Fall 2013.  It is designed to bring the two programs together as both fields require an understanding of the convergence of manifolds and metric measure spaces.  We meet Wednesday afternoons 3-5pm in the Baker Boardroom.

Updated on Sep 20, 2013 02:57 PM PDT
112. # Geroch Lunch Seminar

Location: MSRI: Baker Board Room

The speaker will be chosen among the members of the audience at the time of the event. One or more volunteers from the audience will present a current topic of research, possibly but not necessarily one on which they are currently working.

Updated on Sep 16, 2013 02:52 PM PDT
113. # OT Programmatic Seminar: Multimarginal optimal transport with Coulomb cost

Location: MSRI: Simons Auditorium
Speakers: Maria Colombo (Scuola Normale Superiore)

In some recent papers, a connection between optimal transport and density functional theory has been noticed. The transport model involves a cost function of Coulomb type which decreases with distance. We present some initial results on this multimarginal transport problem. In particular, we introduce a natural notion of cyclical Monge problem and we show the equality between its infimum and the  minimum in the classical Kantorovich problem. Finally, we study the problem in dimension one, building an optimal map.

Updated on Sep 19, 2013 10:33 AM PDT
114. # MGR Programmatic Seminar: On the mass-aspect tensor of asymptotically hyperbolic manifolds

Location: MSRI: Simons Auditorium
Speakers: Julien Cortier (Institut des Hautes Études Scientifiques (IHES))

Asymptotically hyperbolic manifolds appear in many situations in General Relativity, such as isolated systems in a universe with negative cosmological constant and in the AdS/CFT correspondence theory as conformally compact spaces.

As for the ADM mass of asymptotically Euclidean manifolds, one can define mass-like asymptotic invariants. After a review of classical results about these quantities such as positive mass theorems by X. Wang and P.T. Chrusciel - M. Herzlich, we will focus on the mass-aspect tensor that appears in Wang's definition, when the boundary at infinity is assumed to be spherical.

We will give examples for Kottler-Schwarzschild-AdS manifolds as well as a new family which has interesting properties near infinity, such as being conformally flat and of constant scalar curvature. We will finally discuss how to look for new mass-like invariants constructed from the mass-aspect tensor.

This is partly based on a joint work with Mattias Dahl and Romain Gicquaud.

Updated on Sep 06, 2013 09:37 AM PDT
115. # Chancellor's Lecture - Topics in Analysis: Hidden convexity in nonlinear PDES

Location: 51 Evans Hall, UC Berkeley
Speakers: Yann Brenier (École Polytechnique)

Outline: Several examples of hidden convexity in nonlinear PDEs will be addressed. Most of them are related to the theory of “optimal transportation”, which is the theme of one of the two MSRI programs this fall: see http://www.msri.org/programs/277.

1) Fully nonlinear elliptic equations: The canonical example is the reduction of the Monge-Ampere equation (a fully nonlinear elliptic PDE related to the “Minkowski problem” in geometry) to a convex minimization problem, a la Kantorovich, which can be solved by convex duality techniques. Connections with combinatorial optimization and “optimal transport” will be discussed.

2) Mathematical fluid mechanics:
i) Some solutions to the Euler equations can be obtained by using the least action principle (following V.I. Arnold’s geometric interpretation), leading to the problem of “optimal incompressible transport”; this problem has a hidden convex structure which provides existence, uniqueness and partial regularity for its solution.
ii) The hydrostatic and semi-geostrophic limits of the Euler and Navier-Stokes equations are examples of very singular limits that cannot be justified on standard linear functional spaces but can be addressed successfully on suitable convex functional cones.

3) Electromagnetism and magnetohydrodynamics:
i) The nonlinear theory of electromagnetism by Born and Infeld is described by a system of nonlinear conservation laws (which leads to the standard Maxwell equations for fields of low intensity), which has an interesting hidden structure, showing very easily its hyperbolic nature; the high field limit of the BI equations will be discussed and related to the “optimal transport of currents”.
ii) The magnetic relaxation equations proposed by Moffatt can be seen as a natural extension to divergence-free vector fields of the scalar heat equation (following the interpretation of Jordan-Kinderlehrer-Otto); they form a very degenerate parabolic systems of PDEs with a hidden convex structure that enables us to show the global existence of “dissipative solutions” (in the spirit of P.-L. Lions and Ambrosio-Gigli-Savar´e).

Created on Aug 26, 2013 02:27 PM PDT
116. # MSRI/Evans Lecture: On the topology and future stability of the universe

Location: UC Berkeley, 60 Evans Hall
Speakers: Hans Ringström (Royal Institute of Technology (KTH))

The current standard model of the universe is spatially homogeneous, isotropic and spatially flat. Furthermore, the matter content is described by two perfect fluids (dust and radiation) and there is a positive cosmological constant. Such a model can be well approximated by a solution to the Einstein-Vlasov equations with a positive cosmological constant. As a consequence, it is of interest to study stability properties of solutions in the Vlasov setting. The talk will contain a description of recent results on this topic. Moreover, the restriction on the global topology of the universe imposed by the data collected by observers will be discussed.

Updated on Sep 11, 2013 01:02 PM PDT
117. # PD Seminar: On the mass/angular momentum inequality

Location: 939 Evans Hall
Speakers: Xin Zhou (Massachusetts Institute of Technology)
Updated on Sep 13, 2013 10:44 AM PDT
118. # PD Seminar: Multimarginal optimal transport on Riemannian manifolds.

Location: 939 Evans Hall
Speakers: Brendan Pass (University of Alberta)
Updated on Sep 13, 2013 10:42 AM PDT
119. # OT Programmatic Seminar: Type II ancient solutions to the Yamabe flow

Location: MSRI: Simons Auditorium

We will discuss the construction on new Type II compact ancient compact solutions to the  Yamabe flow.  Our solutions are rotationally symmetric and converge, as $t \to -\infty$,  to a tower of N spheres. Their curvature operator changes sign. Our technique may be viewed as a  parabolic analogue of  gluing  two  exact solutions to the rescaled equation, that is the spheres, with narrow cylindrical necks to obtain a new ancient solution to the Yamabe flow.

Updated on Sep 13, 2013 10:11 AM PDT
120. # MGR Programmatic Seminar: The Newtonian Limit of Cosmological Spacetimes

Location: MSRI: Simons Auditorium
Speakers: Todd Oliynyk (Monash University)

In recent years, there has been a resurgence in interest in the relationship between Newtonian gravity and General Relativity on cosmological scales, which is motivated by questions surrounding the physical interpretation of large scale cosmological simulations using Newtonian gravity and the role of Newtonian gravity in cosmological averaging. The overriding fundamental question is in what sense, if any, does Newtonian gravity provide an approximation to General Relativity on a cosmological scale. In this talk, I will describe a wide class of inhomogeneous relativistic solutions that are well approximated on cosmological scales by solutions of Newtonian gravity. The initial value formulation for these solutions will be presented and I will outline the estimates that lead to existence and guarantee convergence to solutions of Newtonian gravity.

Updated on Sep 13, 2013 01:21 PM PDT
121. # Chancellor's Lecture - Topics in Analysis: Hidden convexity in nonlinear PDES

Location: 51 Evans Hall, UC Berkeley
Speakers: Yann Brenier (École Polytechnique)

Outline: Several examples of hidden convexity in nonlinear PDEs will be addressed. Most of them are related to the theory of “optimal transportation”, which is the theme of one of the two MSRI programs this fall: see http://www.msri.org/programs/277.

1) Fully nonlinear elliptic equations: The canonical example is the reduction of the Monge-Ampere equation (a fully nonlinear elliptic PDE related to the “Minkowski problem” in geometry) to a convex minimization problem, a la Kantorovich, which can be solved by convex duality techniques. Connections with combinatorial optimization and “optimal transport” will be discussed.

2) Mathematical fluid mechanics:
i) Some solutions to the Euler equations can be obtained by using the least action principle (following V.I. Arnold’s geometric interpretation), leading to the problem of “optimal incompressible transport”; this problem has a hidden convex structure which provides existence, uniqueness and partial regularity for its solution.
ii) The hydrostatic and semi-geostrophic limits of the Euler and Navier-Stokes equations are examples of very singular limits that cannot be justified on standard linear functional spaces but can be addressed successfully on suitable convex functional cones.

3) Electromagnetism and magnetohydrodynamics:
i) The nonlinear theory of electromagnetism by Born and Infeld is described by a system of nonlinear conservation laws (which leads to the standard Maxwell equations for fields of low intensity), which has an interesting hidden structure, showing very easily its hyperbolic nature; the high field limit of the BI equations will be discussed and related to the “optimal transport of currents”.
ii) The magnetic relaxation equations proposed by Moffatt can be seen as a natural extension to divergence-free vector fields of the scalar heat equation (following the interpretation of Jordan-Kinderlehrer-Otto); they form a very degenerate parabolic systems of PDEs with a hidden convex structure that enables us to show the global existence of “dissipative solutions” (in the spirit of P.-L. Lions and Ambrosio-Gigli-Savar´e).

Created on Aug 26, 2013 02:25 PM PDT
122. # Converging Spaces Reading Seminar

Location: MSRI: Baker Board Room

This seminar is open to all faculty, postdocs and doctoral students involved in either program at MSRI in Fall 2013.  It is designed to bring the two programs together as both fields require an understanding of the convergence of manifolds and metric measure spaces.  We meet Wednesday afternoons 3-5pm in the Baker Boardroom.

Updated on Sep 12, 2013 09:30 AM PDT
123. # Geroch Lunch Seminar

Location: MSRI: Baker Board Room

The speaker will be chosen among the members of the audience at the time of the event. One or more volunteers from the audience will present a current topic of research, possibly but not necessarily one on which they are currently working.

Updated on Sep 16, 2013 02:51 PM PDT
124. # Villani Postdoc/Graduate Student Optimal Transport Seminar: Solution of the Monge problem

Location: MSRI: Baker Board Room
Speakers: Gerolin Augusto (Università di Pisa)
Updated on Sep 13, 2013 10:34 AM PDT
125. # OT Programmatic Seminar: Uniqueness of solutions of Hamilton-Jacobi equations in the space of probability measures.

Location: MSRI: Simons Auditorium
Speakers: Ryan Hynd (University of Pennsylvania)

Hamilton-Jacobi equations (HJE) in the space of measures arise naturally when approximating the dynamics of many particle systems in classical mechanics. At first sight, these equations appear to be very difficult to analyze. We argue, however, that the space of measures has just enough regularity to admit a uniqueness theorem for solutions of these HJE.

Our hope is that the ideas presented in the talk will provide methods for obtaining properties of solutions and in turn information on many particles systems.

Updated on Sep 06, 2013 02:16 PM PDT
126. # MGR Programmatic Seminar: Dynamic and Thermodynamic Stability of Black Holes and Black Branes

Location: MSRI: Simons Auditorium
Speakers: Robert Wald (University of Chicago)

I describe work with with Stefan Hollands that establishes a new criterion for the dynamical stability of black holes in $D \geq 4$ spacetime dimensions in general relativity with respect to axisymmetric perturbations: Positivity of the canonical energy, $\mathcal E$, on a subspace of linearized solutions that have vanishing linearized ADM mass, momentum, and angular momentum at infinity and satisfy certain gauge conditions at the horizon implies mode stability. Conversely, failure of positivity of $\mathcal E$ on this subspace implies the existence of perturbations that cannot asymptotically approach a stationary perturbation. We further show that $\mathcal E$ is related to the second order variations of mass, angular momentum, and horizon area by $\mathcal E = \delta^2 M - \sum_i \Omega_i \delta^2 J_i - (\kappa/8\pi) \delta^2 A$, thereby establishing a close connection between dynamic stability and thermodynamic stability. Thermodynamic instability of a family of black holes need not imply dynamic instability because the perturbations towards other members of the family will not, in general, have vanishing linearized ADM mass and/or angular momentum. However, we prove that all black branes corresponding to thermodynamically unstable black holes are dynamically unstable. We also prove that positivity of $\mathcal E$ is equivalent to the satisfaction of a local Penrose inequality,'' thus showing that satisfaction of this local Penrose inequality is necessary and sufficient for dynamical stability.

Updated on Aug 28, 2013 09:33 AM PDT
127. # Chancellor's Lecture - Topics in Analysis: Hidden convexity in nonlinear PDES

Location: 51 Evans Hall, UC Berkeley
Speakers: Yann Brenier (École Polytechnique)

Outline: Several examples of hidden convexity in nonlinear PDEs will be addressed. Most of them are related to the theory of “optimal transportation”, which is the theme of one of the two MSRI programs this fall: see http://www.msri.org/programs/277.

1) Fully nonlinear elliptic equations: The canonical example is the reduction of the Monge-Ampere equation (a fully nonlinear elliptic PDE related to the “Minkowski problem” in geometry) to a convex minimization problem, a la Kantorovich, which can be solved by convex duality techniques. Connections with combinatorial optimization and “optimal transport” will be discussed.

2) Mathematical fluid mechanics:
i) Some solutions to the Euler equations can be obtained by using the least action principle (following V.I. Arnold’s geometric interpretation), leading to the problem of “optimal incompressible transport”; this problem has a hidden convex structure which provides existence, uniqueness and partial regularity for its solution.
ii) The hydrostatic and semi-geostrophic limits of the Euler and Navier-Stokes equations are examples of very singular limits that cannot be justified on standard linear functional spaces but can be addressed successfully on suitable convex functional cones.

3) Electromagnetism and magnetohydrodynamics:
i) The nonlinear theory of electromagnetism by Born and Infeld is described by a system of nonlinear conservation laws (which leads to the standard Maxwell equations for fields of low intensity), which has an interesting hidden structure, showing very easily its hyperbolic nature; the high field limit of the BI equations will be discussed and related to the “optimal transport of currents”.
ii) The magnetic relaxation equations proposed by Moffatt can be seen as a natural extension to divergence-free vector fields of the scalar heat equation (following the interpretation of Jordan-Kinderlehrer-Otto); they form a very degenerate parabolic systems of PDEs with a hidden convex structure that enables us to show the global existence of “dissipative solutions” (in the spirit of P.-L. Lions and Ambrosio-Gigli-Savar´e).

Updated on Aug 26, 2013 02:24 PM PDT
128. # Villani Postdoc/Graduate Student Optimal Transport Seminar: Displacement Interpolation

Location: MSRI: Baker Board Room
Speakers: Rosemonde Lareau-Dussault (University of Toronto)
Updated on Sep 13, 2013 10:32 AM PDT
129. # 5 Minute Talks

Location: MSRI: Simons Auditorium
Created on Sep 06, 2013 09:50 AM PDT
130. # Villani Postdoc/Graduate Student Optimal Transport Seminar: Kantorovich duality

Location: MSRI: Baker Board Room
Speakers: Alexi Hoeft (Virginia Commonwealth University)
Updated on Sep 13, 2013 10:31 AM PDT
131. # Chancellor's Lecture - Topics in Analysis: Hidden convexity in nonlinear PDES

Location: 51 Evans Hall, UC Berkeley
Speakers: Yann Brenier (École Polytechnique)

Several examples of hidden convexity in nonlinear PDEs will be addressed. Most of them are related to the theory of “optimal transportation”, which is the theme of one of the two MSRI programs this fall: see http://www.msri.org/programs/277.

Thursday Sept 12:

A crash course on rational mechanics (with a personal viewpoint) will relate standard optimal transportation problems to Euler and ideal MHD equations.

Updated on Sep 10, 2013 11:00 AM PDT
132. # Chancellor's Lecture - Topics in Analysis: Hidden convexity in nonlinear PDES

Location: 51 Evans Hall, UC Berkeley
Speakers: Yann Brenier (École Polytechnique)

Several examples of hidden convexity in nonlinear PDEs will be addressed. Most of them are related to the theory of “optimal transportation”, which is the theme of one of the two MSRI programs this fall: see http://www.msri.org/programs/277.

Tuesday Sept 10

The Monge-Ampere second boundary value problem has been related to the Monge-Kantorovich transportation problem. Existence and uniqueness of maps with convex potential between given compactly supported probability measures on R^d are established.

Updated on Sep 10, 2013 10:59 AM PDT
133. # MSRI/Evans Lecture: On the topology of black holes and beyond.

Location: UC Berkeley, 60 Evans Hall
Speakers: Greg Galloway (University of Miami)

In recent years there has been an explosion of interest in black holes in higher dimensional gravity.  This, in particular, has led to questions about the topology of black holes in higher dimensions. In this talk we review Hawking's classical theorem on the topology of black holes in 3+1 dimensions (and its connection to black hole uniqueness) and present a generalization of it to higher dimensions.  The latter is a geometric result which imposes restrictions on the topology of black holes in higher dimensions.  We shall also discuss recent work on the topology of space exterior to a black hole.  This is closely connected to the Principle of Topological Censorship, which roughly asserts that the topology of the region outside of all black holes (and white holes) should be simple.   All of the results to be discussed rely on the recently developed theory of marginally outer trapped surfaces, which are natural spacetime analogues of minimal surfaces in Riemannian geometry.  This talk is based primarily on joint work with Rick Schoen and with Michael Eichmair and Dan Pollack.

Updated on Aug 19, 2013 10:38 AM PDT
134. # OT Programmatic Seminar: Geometric analysis on the space of metric measure space

Location: MSRI: Simons Auditorium
Speakers: Theodor Sturm (Hausdorff Research Institute for Mathematics, University of Bonn)

The space $\mathbb X$ of all metric measure spaces $(X,d,m)$ plays an important r\^ole in image analysis, in the investigation of limits of Riemannnian manifolds and metric graphs as well as in the study of geometric flows that develop singularities. We show that the space $\mathbb X$ -- equipped with the $L^2$-distortion distance $\Delta\!\!\!\!\Delta$ -- is a challenging object of geometric interest in its own. In particular, we show that it has nonnegative curvature in the sense of Alexandrov. Geodesics and tangent spaces are characterized in detail. Moreover, classes of semiconvex functionals and their gradient flows on $\mathbb X$ are presented.

Created on Aug 28, 2013 03:37 PM PDT
135. # MGR Programmatic Seminar: A smallness measure of deviation from Kerr-Newman and applications to black hole uniqueness

Location: MSRI: Simons Auditorium
Speakers: Willie Wong (École Polytechnique Fédérale de Lausanne (EPFL))

In 2007, A. Ionescu and S. Klainerman introduced a new approach to considering the black hole uniqueness problem which is based on a characterisation (which originated in the works of M. Mars and W.

Simon) of the family of Kerr black holes among stationary vacuum solutions of Einstein's equations. In this talk I'll start by giving a review of the black hole uniqueness problem. Then I will review the algebraic properties of general stationary electro-vacuum solutions, which leads us to a characterisation of the Kerr-Newman family. I will conclude with a discussion of how to turn the characterisation into a smallness measure and how this can be used to demonstrate various "perturbative" uniqueness results for Kerr-Newman black holes.

Created on Aug 28, 2013 03:39 PM PDT
136. # Chancellor's Lecture - Topics in Analysis: Hidden convexity in nonlinear PDES

Location: 51 Evans Hall, UC Berkeley
Speakers: Yann Brenier (École Polytechnique)

Several examples of hidden convexity in nonlinear PDEs will be addressed. Most of them are related to the theory of “optimal transportation”, which is the theme of one of the two MSRI programs this fall: see http://www.msri.org/programs/277.

2nd lecture: Thursday Sept 5:

-Monge-Ampere has been related to the Monge-Kantorovich optimization problem, existence and uniqueness of maps with convex potential between given measures has been stated; -A comprehensive proof has been started in the simple case of compactly supported measures, end of the proof due Tuesday Sept 10

Updated on Sep 06, 2013 09:47 AM PDT
137. # Chancellor's Lecture - Topics in Analysis: Hidden convexity in nonlinear PDES

Location: 51 Evans Hall, UC Berkeley
Speakers: Yann Brenier (École Polytechnique)

Several examples of hidden convexity in nonlinear PDEs will be addressed. Most of them are related to the theory of “optimal transportation”, which is the theme of one of the two MSRI programs this fall: see http://www.msri.org/programs/277.

1st lecture: Tuesday Sept 3:

-General introduction to the equations to be discussed:

Monge-Ampere, Euler, Born-Infeld, magnetic relaxation; -Tools we need from Convex analysis: Legendre-Fenchel transforms  and Rockaffellar's duality theorem for Banach spaces.

Updated on Sep 06, 2013 09:46 AM PDT
138. # MSRI/Evans Lecture: Swarming by Nature and by Design

Location: UC Berkeley, 60 Evans Hall
Speakers: Andrea Bertozzi (University of California, Los Angeles)

Swarming by Nature and by Design
Andrea Bertozzi, University of California, Los Angeles

The cohesive movement of a biological population is a commonly observed natural phenomenon. With the advent of platforms of unmanned vehicles, such phenomena have attracted a renewed interest from the engineering community.

This talk will cover a survey of the speakers research and related work in this area ranging from aggregation models in nonlinear partial differential equations to control algorithms and robotic testbed experiments.

We conclude with a discussion of some interesting problems for the mathematics community.

Updated on Aug 12, 2013 02:46 PM PDT
139. # Vanishing and Lifting Reading Seminar

Location: MSRI: Simons Auditorium
Speakers: Karl Schwede (Pennsylvania State University)

A paper of Cascini, Tanaka and Xu.

Updated on May 15, 2013 01:28 PM PDT
140. # Noncommutative Clusters (NAGRT)

Location: MSRI: Simons Auditorium
Speakers: Arkady Berenstein (University of Oregon)

Cluster algebras were introduced by Fomin and Zelevinsky in 2001 and have become an important tool in representation theory, higher category theory, and algebraic/Poisson geometry.

The goal of my talk (based on a joint paper with V. Retakh) is to introduce totally noncommutative clusters and their mutations, which can be viewed as generalizations of both classical" and quantum cluster structures.

Each noncommutative cluster X is built on a torsion-free group G and a certain collection of its automorphisms. We assign to X a noncommutative algebra A(X) related to the group algebra of G, which is an analogue of the cluster algebra, and expect a Noncommutative Laurent Phenomenon to hold in the most of algebras A(X).

Our main examples of "cluster groups" G include principal noncommutative tori which we define for any initial exchange matrix B and noncommutative triangulated groups which we define for all oriented surfaces.

Updated on May 17, 2013 09:57 AM PDT
141. # Untwisting a twisted Calabi-Yau algebra (NAGRT)

Location: MSRI: Simons Auditorium
Speakers: Ulrich Kraehmer (University of Glasgow)

In this joint work with Jake Goodman we show that the crossed product of a twisted Calabi-Yau algebra by its modular (aka Nakayama) automorphism is a Calabi-Yau algebra as was shown before by several authors for various special classes of twisted Calabi-Yau algebras.

Updated on May 17, 2013 09:59 AM PDT
142. # Frobenius Singularity Day

Location: MSRI: Baker Board Room
1:30 - 2:10 PM
A characterization of toric varieties in positive characteristic
Speaker: Piotr Achinger
Abstract: A theorem of J. F. Thomsen states that Frobenius push-forwards of line  bundles on smooth toric varieties are direct sums of line bundles.
Using characterization of toric varieties in terms of their Cox rings,  we show that this property in fact characterizes smooth projective  toric varieties.

2:20 - 3:00 PM
F-signature of a Cartier module
Speaker: Kevin Tucker

3:30 - 4:00 PM
Irrational Hilbert-Kunz multiplicities
Speaker: Holger Brenner
Abstract: A theorem of J. F. Thomsen states that Frobenius push-forwards of line  bundles on smooth toric varieties are direct sums of line bundles.
We show how to get from an artinian module with irrational Hilbert-Kunz multiplicity a local ring with irrational Hilbert-Kunz multiplicity.

Updated on May 17, 2013 05:04 PM PDT
143. # On a conjecture of Derksen about syzygies

Location: MSRI: Simons Auditorium
Speakers: Peter Symonds (University of Manchester)

In 2004 Derksen made a conjecture concerning bounds on the degrees of the generators of the syzygies of a ring of polynomial invariants, the resolution being over a polynomial ring that maps onto the invariants.

We will present a proof of an amended version of this conjecture that only uses elementary homological algebra.

This is joint work with Marc Chardin.

Updated on May 17, 2013 01:31 PM PDT
144. # The category of F-module has finite global dimension (COMMA)

Location: MSRI: Simons Auditorium
Speakers: Linquan Ma (University of Michigan)

We prove some homological properties of the category of Lyubeznik's F-modules. In detail, we show that this category has finite global dimension. And we point out that the injective hull of the residue field, though injective in the category of R-module, is not injective in the category of F-modules.

Updated on May 15, 2013 04:45 PM PDT
145. # Connectedness Theorems (COMMA)

Location: MSRI: Simons Auditorium
Speakers: Wenliang Zhang (University of Nebraska)

Hartshorne's Connectedness Theorem asserts that, if a local ring (R,m) has depth at least 2, then Spec(R)\{m} is connected. On the other hand, Faltings' Connectedness Theorem says, if an ideal I of a d-dimensional complete local domain (R,m) can be generated by d-2 elements, then Spec(R/I)\{m} is connected.

Updated on May 13, 2013 10:53 AM PDT
146. # Growth of groups using Euler characteristics

Location: MSRI: Simons Auditorium
Speakers: Alexander Young (University of Washington)

A new method, currently under development, is brought forward to establish an upper bound on the growth of any finitely generated group, using a variant of monoid categories and analagous CW-complexes.

Updated on May 10, 2013 10:59 AM PDT
147. # Totally nonnegative matrices: efficient cell recognition (NAGRT)

Location: MSRI: Simons Auditorium
Speakers: tom Lenagan

A real matrix is totally positive if all of its minors are greater than zero, and, more generally, is totally nonnegative if all of its minors are nonnegative.

There is a cell decomposition of the space of totally nonnegative matrices of a given size, and the set of totally positive matrices forms the big cell in this decomposition. There are well-known efficient criteria for recognising total positivity, but until recently not for the other cells.

In this talk, I'll introduce some of the main ideas concerning totally nonnegative matrices, and then discuss the cell recognition problem, and give a solution that was motivated by connections with the theory of torus invariant prime ideals in quantum matrices.

This is joint work with Ken Goodearl and Stephane Launois.

Updated on May 10, 2013 11:31 AM PDT
148. # Gorenstein liaison of algebraic varieties (COMMA)

Location: MSRI: Simons Auditorium
Speakers: Robin Hartshorne

We will review the definition and basic facts about Gorenstein liaison of varieties in projective space. Taking the case of codimension 2, which is well understood, as a paradigm, we will consider the questions that arise in higher codimensions. A major problem is whether every arithmetically Cohen-Macaulay variety is in the Gorenstein liaison class of a complete intersection (in acronyms: does ACM => glicci?). While this has been proved to be so in many particular cases, the problem is open in general. We will examine some known cases and two striking recent results in the hope of clarifying where the difficulty lies.
Updated on Apr 22, 2013 08:20 AM PDT
149. # Invariant Theory of AS Regular Algebras: AS Gorenstein fixed subrings (NAGRT)

Location: MSRI: Simons Auditorium
Speakers: Ellen Kirkman (Wake Forest University)

Let $k$ be an algebraically closed field of characteristic zero, $A$  be an Artin-Schelter regular algebra, and $G$ be a group of graded automorphisms of $A$.  J{\o}rgensen and Zhang proved that if all elements of $G$ have homological determinant 1, then $A^G$ is Artin-Schelter Gorenstein.  For a family of AS regular algebras of dimension 3 (the Noetherian graded down-up algebras) we determine when $A^G$ is a complete intersection" (in a sense to be defined), and we relate this condition to the form of the Hilbert series of $A^G$, and to generators of $G$.  For this class of algebras, we obtain an extension to $A$ of a theorem for $k[x_1, \cdots, x_n]$ due to Kac-Watanabe and Gordeev.

(This is joint work with James Kuzmanovich and James Zhang).

Updated on May 10, 2013 11:30 AM PDT
150. # Deformation of F-Injective Singularities (COMMA)

Location: MSRI: Simons Auditorium
Speakers: Lance Miller (University of Utah)

It is a long standing conjecture that F-injectivity deforms. In this talk, we discuss some simple criteria on local cohomology sufficient to give that F-injectivity deforms. These will apply to show that F-injectivity deforms when the non-CM locus of the special fiber is isolated and that F-purity deforms to F-injectivity.. This is joint work with Kazuma Shimomoto and Jun Horiuchi.

Updated on May 09, 2013 10:05 AM PDT
151. # MSRI/NRing Women in Math Lunch

Location: MSRI: Baker Board Room
Updated on May 03, 2013 01:38 PM PDT
152. # Commutative Algebra and Algebraic Geometry (Eisenbud Seminar)

Location: UC Berkeley

Commutative Algebra and Algebraic Geometry Seminar
Tuesdays, 3:45-6:00
939 Evans Hall

Organized by David Eisenbud
Updated on Feb 05, 2013 02:24 AM PST
153. # Orders in the elliptic Weyl algebra

Location: MSRI: Baker Board Room
Speakers: Susan Sierra (University of Edinburgh)

An "elliptic Weyl algebra" is obtained by localising a (generic) Sklyanin algebra at the central element g.  It is a hereditary domain of GK-dimension 2 that has the surprising and beautiful property that all of its subalgebras are finitely generated and noetherian.  We present the classification of maximal orders in elliptic Weyl algebras and give some consequences, focusing on the ideal structure.  We show that any order in an elliptic Weyl algebra has DCC on ideals, and deduce that any graded order in (the 3rd Veronese of) a Sklyanin algebra must be noetherian.  This is joint work with Dan Rogalski and Toby Stafford.

Updated on May 02, 2013 12:06 PM PDT
154. # Algebra and Algebraic Geometry Seminar (COMMA)

Location: UC Berkeley
Speakers: Adam Boocher (University of California, Berkeley), Justin Chen (University of California, Berkeley)
Updated on May 02, 2013 12:29 AM PDT
155. # On Fourier-Mukai type functors (NAGRT)

Location: MSRI: Simons Auditorium
Speakers: Alice Rizzardo (International School for Advanced Studies (SISSA/ISAS))

Orlov showed in 1997 that all exact, fully faithful functors between the bounded derived categories of two smooth projective varieties are isomorphic to a Fourier-Mukai transform. In this talk we will discuss what happens when removing the fullness and faithfulness hypotheses.

Updated on May 01, 2013 12:20 PM PDT
156. # Lyubeznik-like invariants of local rings of mixed characteristic (COMMA)

Location: MSRI: Simons Auditorium
Speakers: Emily Witt (University of Minnesota Twin Cities)

The Lyubeznik numbers are a family of invariants of a local ring containing a field that detect many ring-theoretic properties, and also have topological and geometric interpretations.  Motivated by their utility, in joint work with Luis Núñez-Betancourt, we define a new family of invariants of any local ring with characteristic p>0 residue field; in particular, they are defined for local rings of mixed characteristic.  For local rings of equal characteristic p>0, both the Lyubeznik numbers and these new invariants are defined.  In some cases, they agree, but we give an example where they differ.

Updated on Apr 29, 2013 01:56 PM PDT
157. # Hamiltonian flow on complete intersections (NAGRT)

Location: MSRI: Simons Auditorium
Speakers: Travis Schedler (University of Illinois)

I compute the coinvariants of functions under Hamiltonian flow for complete intersections with isolated singularities. For surfaces the Hamiltonian flow is with respect to the Jacobian Poisson structure; in higher dimensions the Hamiltonian flow can be generalized using the natural top polyvector field which can be thought of as a degenerate Calabi-Yau structure. In particular the dimension of the coinvariant space equals the sum of the dimension of the top cohomology of the singular variety with the sum of the Milnor numbers of the singularities. In other words this equals the top cohomology of the smoothing of the variety. These results follow from more general ones computing the D-module which represents invariants under the Hamiltonian flow. The structure is interesting: it turns out to have a summand which is the maximal extension on the bottom, but not on the top, of the intersection cohomology D-module. This is joint work with Pavel Etingof.

Updated on May 01, 2013 11:49 AM PDT
158. # How the P versus NP problem manifests itself in invariant theory (COMMA)

Location: MSRI: Simons Auditorium
Speakers: Jerzy Weyman (Northeastern University)

Mulmuley and Sohoni came up with the approach to the Valiant version of the P versus NP problem using invariant theory. This approach leads to interesting questions related to the orbit closures of the algebraic group actions. It also shows that the P versus NP problem is closely related to two classical problems in representation theory of the general linear group. In this talk, I will discuss these connections and point out some easier problems that might be of interest to commutative algebraists.

Updated on May 01, 2013 11:48 AM PDT
159. # Commutative Algebra and Algebraic Geometry (Eisenbud Seminar)

Location: UC Berkeley
Speakers: Persi Diaconis (Stanford University), David Eisenbud (MSRI - Mathematical Sciences Research Institute)

Commutative Algebra and Algebraic Geometry Seminar
Tuesdays, 3:45-6:00
939 Evans Hall

Organized by David Eisenbud
More information at http://hosted.msri.org/alg/ 3:45 PM Quantitative Cocycles Speaker: Persi Diaconis Abstract: Choosing sections for natural maps is a basic mathematical activity. In joint work with Soundarajan and Shao we study the problem of choosing "nice" sections. Here is a typical theorem: Let $G$ be a finite group, $H$ a normal subgroup. Let $X$ be coset representatives for $H$ in $G$. suppose the proportion of $x,y$ in $X$ with $xy \in X$ is more than $1-1/60$. Then the extension splits. There are many variations, many open problems and applications to basic arithmetic and computer science. 5:00 PM Clifford Algebras and the Ranks of Modules in Free Resolutions Speaker: David Eisenbud Abstract: A conjecture of Horrocks, and independently of Buchsbaum and myself, asserts that the sum of the ranks of the modules in the free resolution of a module annihilated by a regular sequence of length c is at least $2^{c}$. I'll describe a related new conjecture by Irena Peeva and myself and show how we proved a special case, in our work on complete intersections, using results on Clfford algebras and enveloping algebras.

Updated on May 01, 2013 11:48 AM PDT
160. # Hochschild-Witt homology (NAGRT)

Location: MSRI: Simons Auditorium
Speakers: Dmitry Kaledin (Independent University of Moscow)

I am going to describe Hochschild-Witt homology, a new homology theory for associative algebras and DG algebras over a finite field that extends crystalline cohomology to the non-commutative setting. This is based on reexamination and generalization of the classical notion of Witt vectors. Using this, we introduce what we call a Hochschild-Witt complex, a gadget refining the usual Hochschild homology complex of an algebra in exactly the same way as the de Rham-Witt complex of Deligne and Illusie refines the usual de Rham complex of a smooth algebraic variety over a finite field.

Updated on May 01, 2013 11:47 AM PDT
161. # A motivic approach to Potts models

Location: UC Berkeley, 60 Evans Hall
Speakers: Matilde Marcolli

The use of motivic techniques in Quantum Field Theory has been widely explored in the past ten years, in relation to the occurrence of periods in the computation of Feynman integrals. In this lecture, based on joint work with Aluffi, I will show how some of these techniques can be extended to a motivic analysis of the partition function of Potts models in statistical mechanics. An estimate of the complexity of the locus of zeros of the partition function, can be obtained in terms of the classes in the Grothendieck ring of the affine algebraic varieties defined by the vanishing of the multivariate Tutte polynomial, based on a deletion-contraction formula for the Grothendieck classes.
Updated on Apr 15, 2013 06:42 AM PDT
162. # On generalized Hilbert-Kunz function and multiplicity (COMMA)

Location: MSRI: Simons Auditorium
Speakers: Hailong Dao (University of Kansas)

Let (R, m) be a local ring of characteristic p with perfect residue field. Let I be an ideal of R. In this talk I will describe some recent results, joint with Ilya Smirnov and Keiichi Watanabe, on the asymptotic behavior of length of the zeroth local cohomology module of R/I^[q]. This is an obvious generalization of the classical concepts of Hilbert-Kunz function and multiplicity.

Updated on May 01, 2013 11:46 AM PDT
163. # Representation theory of Hecke algebras and connections with Cherednik algebras (NAGRT)

Location: MSRI: Simons Auditorium
Speakers: Maria Chlouveraki (Université Versailles/Saint Quentin-en-Yvelines)

Hecke algebras associated with Weyl groups appear naturally as endomorphism rings in the study of finite reductive groups. Broué, Malle and Rouquier have generalized their definition to all complex reflection groups. Hecke algebras depend on a parameter q and their representation theory becomes very interesting when q specializes to a root of unity. The existence of canonical basic sets and the cellular algebra structure have been key elements in the understanding of the representation theory of Hecke algebras in that case. An open question is whether these structures exist for any choice of parameters and for all complex reflection groups. In this talk will see how the connections with the representation theory of rational Cherednik algebras, another type of algebras associated with complex reflection groups, could provide an answer to this problem.
Updated on Jul 17, 2013 10:48 AM PDT
164. # An introduction to certain Frobenius invariants (COMMA)

Location: MSRI: Simons Auditorium
Speakers: Daniel Hernandez (University of Minnesota Twin Cities)

In this talk, we will discuss certain invariants of hypersurfaces defined via the Frobenius endomorphism in characteristic p. In addition to presenting lots of examples, we will also recall the relationship between these invariants and ones arising in the characteristic zero setting (e.g., log canonical thresholds and Bernstein-Sato polynomials). *Warning*: This talk will be more of an elementary, colloquium-style overview than a serious research talk, and will not be aimed towards experts. In particular, we hope to make it accessible to postdocs from both programs. Though we will discuss some recent results, we will probably not prove anything.
Updated on May 24, 2013 12:41 PM PDT
165. # Overview of Combinatorial Game Theory

Location: MSRI: Simons Auditorium
Speakers: Elwyn Berlekamp

This talk will present an overview of the Theory of Combinatorial Games (CG)

In 1901, a Harvard math professor named Bouton published his mathematical solution to the then-popular barroom game called Nim.
This marked the birth of a subject call combinatorial game theory, which seeks to determine optimal strategies for positions in board games. The theory has been most successful for games whose positions tend to breakup into disjoint regions, which are treated as sums.
Examples of such games include classics such as Go, Dots-and-Boxes, Fox-and-Geese, and Konane (also known as Hawaiian checkers), as well as more modern games such as Domineering, Hackenbush, Amazons, and Clobber.
Combinatorial Game Theory yields insights into endgame positions in all of these games, as well as a few special positions in chess and Anglo-American checkers.

The mathematical emphasis of the theory is on a partial order and the behavior of equivalence classes of combinatorial game positions under the operation of addition. This enables CG to be treated as a large commutative monoid, which contains some well-known groups. The dyadic rationals appear immediately, and provide numerical bounds on all other CG. Among the most interesting CG are the infinitesimals. One common class of infinitesimals is the nimbers, a countably infinite group in which every element has order two. There is also a first order of infinitesimals, and many higher orders, none of which can be viewed as the "second" order. By allowing games with infinitely many positions while imposing other severe restrictions, one obtains Conway\'s elegant constructions of the real, transfinite, and surreal numbers.

The set of finite CG also naturally contains several idempotents with useful properties. And more: There are some powerful theorems which can be viewed as properties of other "contrived" idempotents.

This talk will explain some of these results. No prior background is assumed.
Updated on Apr 19, 2013 08:04 AM PDT
166. # Defining a Notion of Noncommutative Complete Intersection via Point Modules (NAGRT)

Location: MSRI: Simons Auditorium
Speakers: Michaela Vancliff

This talk will focus in part on joint work with T. Cassidy regarding a definition of complete intersection using point modules in the context of skew polynomial rings.
The hurdles involved in extending the definition to some other types of algebras will then be explored.
Updated on Apr 30, 2013 04:45 PM PDT
167. # Various uniform bounds for very ample line bundles on toric varieties (COMMA)

Location: MSRI: Simons Auditorium

For any field, we produce an explicit series 4-dimensional domains which are homogeneous graded algebras over the field and whose normalizations (i) have the same degree 1 components as the original algebras, (ii) are generated as algebras in degrees at most 2, yet (iii) admit no uniform upper bound for the discrepancy between the Hilbert functions and the Hilbert polynomials, when viewed as modules over the original homogeneous algebras. The natural habitat of this sort of phenomena is very ample line bundles on projective toric varieties. In the talk, we will overview various related uniform bounds in the homological and combinatorial theory of the rings of sections of such line bundles, some known to exist and some conjectured. Most of these results are joint works with Bruns, Trung, Beck, and Delgado.
Updated on Apr 18, 2013 10:15 AM PDT
168. # F-singularities reading seminar: Vanishing theorems and lifting

Location: MSRI: Simons Auditorium
Speakers: Karl Schwede (Pennsylvania State University)

Updated on May 24, 2013 10:36 AM PDT
169. # Commutative Algebra and Algebraic Geometry (Eisenbud Seminar)

Location: UC Berkeley

Commutative Algebra and Algebraic Geometry Seminar
Tuesdays, 3:45-6:00
939 Evans Hall

Organized by David Eisenbud
More information at http://hosted.msri.org/alg/ 3:45 PM Finite criteria for a ring to be Golod Speaker: Luchezar Avramov Abstract: Golod rings can be characterized by a numerical condition on the Betti numbers of the residue class field, or by a homological condition on the products in Koszul homology. The original proof of the equivalence shows that each condition can be checked in a known number of steps, but many subsequent proofs do not provide such information. The talk will explain a proof that does. 5 PM Sharp upper bounds for higher linear syzygies of projective varieties Speaker: Kangjin Han Abstract: In this talk, we are going to consider upper bounds of higher linear syzygies i.e. graded Betti numbers in the first linear strand of the minimal free resolutions of projective varieties in arbitrary characteristic. For this purpose, we first remind Partial Elimination Ideals (PEIs)' theory and introduce a new framework in which one can study the syzygies of embedded projective schemes well using PEIs theory and the reduction method via inner projections. Next we establish quite useful inqualities which govern the relations between the graded Betti numbers in the first linear strand of an algebraic set $X\subset\mathbb{P}^{N}$ and the ones of its inner projection $X_q\subset\mathbb{P}^{N-1}$. Using these results, we obtain some natural sharp upper bounds for higher linear syzygies of any nondegenerate projective variety in terms of the codimension with respect to its own embedding and classify what the extremal case and next to the extremal case are. This gives us interesting generalizations of classical characterizations on varieties of small degree by Castelnuovo and Fano from the viewpoint of syzygies'. Note that our method could be also applied to get similar results for more general categories (e.g. connected in codimension one algebraic sets). This is a joint work with Sijong Kwak.
Updated on Apr 19, 2013 02:45 AM PDT
170. # Noncommutative deformations of curves and spherical twists (NAGRT)

Location: MSRI: Simons Auditorium
Speakers: Michael Wemyss (University of Edinburgh)

I will explain why, when studying derived autoequivalences of 3-folds, it is necessary to understand noncommutative deformations of curves. In the talk I will give a construction of a certain "noncommutative twist" associated to any floppable curve that recovers the flop-flop functor on the level of the derived category. The idea is that the commutative deformation base is too small for the homological algebra to work, so we need to fatten it by considering noncommutative directions. Our construction generalizes work of Seidel--Thomas and Toda who considered the special case when the curve deforms in only one direction. I will try to explain why considering noncommutative deformations is strictly necessary, as I will show that considering only the commutative deformations does not give a derived autoequivalence as one might hope. This all sounds very fancy, but the talk will be based around one basic example, where the birational geometry of a certain 3-fold is controlled by the cusp in the quantum plane, which is a 9-dimensional self-injective algebra. This is all based on joint work with Will Donovan.
Updated on Sep 11, 2013 10:23 AM PDT
171. # Opening of Frobenius Topics

Location: MSRI: Simons Auditorium

Updated on Apr 18, 2013 04:10 AM PDT
172. # Autoequivalences arising from variation of GIT (NAGRT)

Location: MSRI: Simons Auditorium
Speakers: Ian Shipman (University of Michigan)

Recently there has been an advance in understanding the relationship between the derived categories of the stack quotient of a variety X by a group G and its GIT quotients. I will explain the connection. Then I will present joint work with Dan Halpern-Leistner on how a variation of GIT can be used to produce autoequivalences, which turn out to be special. Along the way, we will see a tight connection between spherical functors and mutations of semiorthogonal decompositions. If time and courage permit, I will remark on how our results confirm a prediction from mirror symmetry.
Updated on May 17, 2013 04:45 PM PDT
173. # Some results on local cohomology in positive characteristic (COMMA)

Location: MSRI: Simons Auditorium
Speakers: Yi Zhang (University of Illinois at Urbana-Champaign)

Let $R=k[x_1,\cdots, x_n]$ be a polynomial ring over a field $k$ of characteristic $p>0.$ If $I$ is an ideal of $R,$ we denote $H^i_I(R)$ the $i$-th local cohomology module of $R$ with support in $I.$ After some introductory material on local cohomology, we will give a lower bound of the dimension of associated primes $P$ of $H^i_I(R)$ in terms of the degrees of the generators of $I.$ Let $\m=(x_1,\cdots, x_n)$ be the maximal ideal generated by the variables and let $I_1,\cdots, I_s$ be homogeneous ideals of $R.$ We will describe the grading of $H^i_{\mathfrak{m}}(H^{j_1}_{I_1}\circ\cdots \circ H^{j_s}_{I_s}(R))$ and also give two algorithms to calculate it.
Updated on Sep 09, 2013 09:47 AM PDT
174. # 2013 Chern Lectures: Correspondences.

Location: UC Berkeley, 60 Evans Hall
Speakers: Nigel Hitchin

Updated on Apr 10, 2013 07:12 AM PDT
175. # COMMA Local Cohomology Day

Location: MSRI: Simons Auditorium

10:00 - 11:00 AM Cohomological and homogeneity conditions on the Jacobian of a polynomial Speaker: Uli Walther Abstract: The free resolution of the Jacobian ideal of a polynomial contains a lot of geometric information on the hypersurface. "Freeness" arises if the resolution is as short as it can be (barring smoothness). We discuss natural sources, weakenings, and implications of freeness under varying homogeneity conditions. 11:30 AM - 12:30 PM Associated primes of local cohomology modules Speaker: Gennady Lyubeznik Abstract: : I will give a survey of work on associated primes of local cohomology modules, including the very latest results. 2:00 - 3:00 PM Regularity of group cohomology Speaker: Peter Symonds Abstract: We will survey what is known about local cohomology and regularity of cohomology rings of groups and invariants.
Updated on Apr 11, 2013 08:44 AM PDT
176. # Geigle-Lenzing spaces, d-canonical algebras and d-representation infinite algebras (NAGRT)

Location: MSRI: Simons Auditorium
Speakers: Osamu Iyama

There are two fundamental classes of objects in representation theory: path algebras of quivers and Geigle-Lenzing's weighted projective lines (or derived equivalently, Ringel's canonical algebras). Their importance comes from the fact that they give rise to abelian categories of global dimension 1. The aim of this talk is to consider higher dimensional analogs of these objects.
Updated on Apr 11, 2013 03:05 AM PDT
177. # Adjoint associativity: an invitation to higher algebra (COMMA)

Location: MSRI: Simons Auditorium
Speakers: Joseph Lipman (Purdue University)

There appeared not long ago a Reduction Formula for derived Hochschild (co)homology, that has been useful e.g., in the study of Gorenstein maps and of rigidity w.r.t. semidualizing complexes. The formula involves the relative dualizing complex of a map, and so brings out a connection between Hochschild homology and Grothendieck duality. The proof, somewhat ad hoc, uses homotopical considerations via numerous non canonical resolutions, both projective and injective, of differential graded objects. Recent efforts are producing more intrinsic approaches, which one hopes to upgrade to "higher" contexts, for example bimodules over algebras in infinity categories. This would lead to wider applicability, for example, to ring spectra; and the methods might be globalizable, revealing some homotopical generalizations of Grothendieck duality. (The original formula has a geometric version, proved by completely different methods coming from duality theory.) After reviewing the formula, I will just try to explain a few elementary things about infinity categories, and how one can express therein the basic relation (adjoint associativity) between Hom and tensor products that underlies any proof.
Updated on May 06, 2013 01:09 PM PDT
178. # 2013 Chern Lectures: Twistors and holomorphic geometry.

Location: UC Berkeley
Speakers: Nigel Hitchin

Updated on Apr 10, 2013 07:12 AM PDT
179. # Commutative Algebra and Algebraic Geometry (Eisenbud Seminar)

Location: UC Berkeley

Commutative Algebra and Algebraic Geometry Seminar
Tuesdays, 3:45-4:45
939 Evans Hall

Organized by David Eisenbud

3:45 PM
Speaker: Vu Thanh
Koszul algebras and the Frobenius endomorphisms
Abstract: Let $R$ be a standard graded algebra over a field of characteristic $p > 0$. Let $\phi:R\to R$ be the Frobenius endomorphism. For each finitely generated graded $R$-module $M$, let $^{\phi}M$ be the abelian group $M$ with an $R$-module structure induced by the Frobenius endomorphism. The $R$-module $^{\phi}M$ has a natural grading given by $\deg x=j$ if $x\in M_{jp+i}$ for some $0\le i \le p-1$. In this talk, I\\'ll discuss our new characterization of Koszul algebras saying that $R$ is Koszul if and only if there exists a non-zero finitely generated graded $R$-module $M$ such that $\reg_R \up{\phi}M <\infty$. This is a joint work with Hop Nguyen.
Updated on Apr 16, 2013 03:02 AM PDT
180. # Speculations on A-Hilb CC^4 for some diagonal Abelian groups A in SL(4), and on Hilb^n CC^3 (NAGRT)

Location: MSRI: Simons Auditorium
Speakers: Miles Reid

Question: for A in SL(4), when does CC^4/A have a crepant resolution? If you expect Calabi-Yau 4-fold geometry to be analogous to the 3-fold case you are probably in for a disappointment. Even in cases when a crepant resolution exists, A-Hilb CC^4 may be bad, for example containing exuberant components. In the longer term, this may be a test case for derived geometry. I will give some algorithms and examples, and suggest some questions on relations between A-Hilb CC^4 computed in toric geometry and Hilb^n CC^3. This is speculative material, so don't expect any of it to be correct. For related material, see our website www.warwick.ac.uk/staff/T.Logvinenko/Traps
Updated on Apr 11, 2013 03:04 AM PDT
181. # F-singularities organizational meeting

Location: MSRI: Baker Board Room

An organizational meeting to discuss working groups for upcoming focus periods
Updated on Apr 12, 2013 08:51 AM PDT
182. # Local cohomology with support in ideals of maximal minors and sub-maximal Pfaffians (COMMA)

Location: MSRI: Simons Auditorium
Speakers: Jerzy Weyman (Northeastern University)

I will report on joint work with Claudiu Raicu and Emily Witt on computing the GL-equivariant description of the local cohomology modules with support in the ideal of maximal minors of a generic matrix. I will explain the main tools that we employ in our study, namely (1) the BGG correspondence between the homology groups of linear complexes over a polynomial ring and minimal free resolutions over the exterior algebra, and (2) the exterior algebra analogue of the geometric technique for computing syzygies. If time permits, I will mention how the same techniques apply to give the description of the local cohomology modules with support in the ideal of 2n x 2n Pfaffians of a (2n+1) x (2n+1) generic skew-symmetric matrix, and mention a possible approach to extend our results to the case of non-maximal minors.
Updated on May 24, 2013 12:38 PM PDT
183. # MSRI/NRing Women in Math Lunch

Location: MSRI: Baker Board Room

Updated on Mar 07, 2013 02:02 AM PST
184. # The 2013 Chern Lectures: Moduli spaces

Location: UC Berkeley, 60 Evans Hall
Speakers: Nigel Hitchin

Updated on Apr 05, 2013 06:14 AM PDT
185. # Gorenstein in codimension 4, applications and the general theory (COMMA)

Location: MSRI: Baker Board Room
Speakers: Miles Reid

I describe the projective resolution of a codimension 4 Gorenstein ideal, aiming to extend Buchsbaum and Eisenbud's famous result in codimension 3. The main result is a structure theorem stating that the ideal is determined by its (k+1) x 2k matrix of first syzygies, viewed as a morphism from the ambient regular space to the Spin-Hom variety SpH_k in Mat(k+1, 2k). This is a general result encapsulating some theoretical aspects of the problem, but, as it stands, is still some way from tractable applications.
Updated on Apr 03, 2013 06:28 AM PDT
186. # The 2013 Chern Lectures: Quaternionic manifolds

Location: UC Berkeley
Speakers: Nigel Hitchen (Oxford University)

Updated on Apr 05, 2013 06:04 AM PDT
187. # Commutative Algebra and Algebraic Geometry (Eisenbud Seminar)

Location: UC Berkeley
Speakers: Oren Ben-Bassat (University of Oxford)

Commutative Algebra and Algebraic Geometry Seminar
Tuesdays, 3:45-6:00
939 Evans Hall

Organized by David Eisenbud
More information at http://hosted.msri.org/alg/ Differential Graded Categories and Milnor's Theorem Oren Ben-Basset (Oxford) In his book on Algebraic K-theory, Milnor gave a technique for gluing projective modules. This technique constructs a projective module on a ring A out of a projective modules on rings B and C and a certain isomorphism. In joint work with Jonathan Block, we generalized this construction to a gluing (involving a homotopy fiber product) of certain differential graded categories. In this talk, I will review differential graded categories and introduce the construction of Jonathan Block which assigns a differential graded category to each differential graded algebra. This construction is fundamentally different than a well known construction involving differential graded modules. If time permits I will give some geometric consequences relating to compact complex manifolds. One of these consequences relates to forming vector bundles on a complex manifold X out of vector bundles "near" a submanifold Z and vector bundles on X-Z. I will also mention a related gluing construction involving gluing categories of coherent sheaves over a punctured formal neighborhood of a subvariety Z inside a variety X over any field k. The punctured formal neighborhood is described using Berkovich analytic geometry. That construction is joint work with Michael Temkin.
Updated on May 15, 2013 12:56 AM PDT
188. # Some examples, theorems, and problems on asymptotic regularity (COMMA)

Location: MSRI: Baker Board Room
Speakers: Steven Cutkosky (University of Missouri)

We discuss the asymptotic regularity of high powers of an ideal, and various saturations of powers of an ideal. We give some illustrative examples, say something about what is known, and speculate on what is not known.
Updated on May 13, 2013 04:20 PM PDT
189. # New examples of hereditary categories with Serre duality (NAGRT)

Location: MSRI: Baker Board Room
Speakers: Adam-Christiaan van Roosmalen (University of Regina)

I will talk about a recent classification of abelian hereditary numerically finite categories with Serre duality, up to derived equivalence. In that classification, one distinguished three main types. The focus of the talk will lie on giving examples of each of these three types, and new examples that occur when one removes the condition that these categories need to be numerically finite.
Updated on May 23, 2013 11:01 AM PDT
190. # Category O over symplectic reflection algebras: a diagrammatic approach (NAGRT)

Location: MSRI: Baker Board Room
Speakers: Benjamin Webster

Abstract: I'll describe a new perspective on the category O over symplectic reflections algebras for the groups $Z/\ell Z \wr S_n$, using ideas from the theory of categorical actions of Lie algebras. This builds on earlier work of Rouquier, Shan, Vasserot, Losev and others, but takes a more explicit diagrammatic perspective. In particular, I'll give an explicitly presented finite dimensional algebra (generalizing KLR algebras) whose representation category is the same as a block of the SRA category O mentioned above.

This algebra is quite interesting in its own right (for example, it is cellular), but it also allows hands-on proofs of several facts which are hard to see from the SRA perspective:

* it is manifestly graded, and thus provides a grading on category O

* the derived equivalences between blocks predicted by Rouquier are
given by easily guessed bimodules

* the identification of decomposition numbers with coefficients of a
canonical basis follows from the application of well-established
techniques from geometric representation theory, for example, from
Varagnolo and Vasserot's proof that projective modules over KLR
algebras give the canonical basis.

I'll try to convince you that this is a fruitful perspective and indicate avenues for better understanding its ties to other approaches to these categories.
Updated on Apr 01, 2013 06:10 AM PDT
191. # DQ-modules on bionic symplectic manifolds

Location: MSRI: Baker Board Room
Speakers: Gwyn Bellamy

Bionic symplectic manifolds are smooth symplectic varieties equipped with a particularly good action of a 2-torus.
These spaces arise naturally in geometric representation theory, for instance when studying rational Cherednik algebras or W-algebras. In this talk I will describe how one can use the bionic structure to learn a great deal about the categories of deformation-quantization modules on these spaces. For instance, one can calculate the K-theory and Hochschild (co)-homology of these categories. The talk is based on joint work in progress with C. Dodd, K. McGerty and T. Nevins.
Updated on Mar 28, 2013 09:36 AM PDT
192. # Superduality

Location: MSRI: Baker Board Room
Speakers: Steven Sam (University of California, Berkeley)

Updated on May 23, 2013 12:44 PM PDT
193. # Commutative Algebra and Algebraic Geometry (Eisenbud Seminar)

Location: UC Berkeley

Commutative Algebra and Algebraic Geometry Seminar
Tuesdays, 3:45-6:00
939 Evans Hall

Organized by David Eisenbud
More information at http://hosted.msri.org/alg/ 3:45 PM: Links and resolutions of rational and Cohen-Macaulay singularities J'anos Koll'ar We study the connection between algebraic properties of singularities and the topology of their links and their resolutions. 5:00PM: Tropicalization of classical moduli spaces Qingchun Ren The image of the complement of a hyperplane arrangement under a monomial map can be tropicalized combinatorially using matroid theory. We apply this to classical moduli spaces that are associated with complex reflection arrangements. Starting from modular curves, we visit the Segre cubic, the Igusa quartic, and moduli of marked del Pezzo surfaces of degrees 2 and 3. Our primary example is the Burkhardt quartic, whose tropicalization is a 3-dimensional fan in 39-dimensional space. This effectuates a synthesis of concrete and abstract approaches to tropical moduli of genus 2 curves. (Work with Steven Sam and Bernd Sturmfels)
Updated on Mar 28, 2013 06:41 AM PDT
194. # Irreducible components of varieties of representations (NAGRT)

Location: MSRI: Simons Auditorium
Speakers: Birge Huisgen-Zimmermann

Let  be a finite dimensional algebra over an algebraically closed field, and Rep(, d) the standard affine variety parametrizing the isomorphism classes of -modules with dimension vector d. We will address the problem of determining the irreducible componentsof the Rep(, d) in terms of representation-theoretic invariants, and of exploring the generic structure of the modules these components encode. After giving an overview of existing theory, stemming from work of Kac, Schofield, Schr¨oer, Crawley-Boevey, Riedtmann, among others, we will present new results. We will conclude with a conjecture addressing the next plausible step in trying to push beyond the status quo.
Updated on Mar 28, 2013 04:56 AM PDT
195. # Hochster's Theta Pairing for Matrix Factorizations

Location: MSRI: Baker Board Room
Speakers: Ragnar-Olaf Buchweitz (University of Toronto)

Hochster noted that the eventual 2-periodicity of projective resolutions over hypersurface rings can be used to define a stable intersection pairing.
We will discuss this notion and show how it links to various geometric and topological incarnations.
Updated on Sep 18, 2013 02:29 PM PDT
196. # From Linear Algebra to Noncommutative Resolutions of Singularities (No April Fools\\' Joke!)

Location: UC Berkeley, 60 Evans Hall
Speakers: Ragnar-Olaf Buchweitz (University of Toronto)

Ten years ago, G.Bergman asked: "Can one factor the classical adjoint of a generic matrix?"
With G.Leuschke we showed that, yes, sometimes you can. We arrived at this by translating the question into one on morphisms between matrix factorizations of the determinant.

Understanding all such morphisms lead through joint work with Leuschke and van den Bergh to a description of a noncommutative desingularization of determinantal varieties in a characteristic-free way and we are just about to put the finishing touches on this work here at MSRI.

I will desribe the highlights of this journey and mention some resulting, and remaining open questions.
Updated on Sep 18, 2013 02:29 PM PDT
197. # Introduction to Castelnuovo-Mumford regularity (COMMA)

Location: MSRI: Simons Auditorium
Speakers: Marc Chardin

In this talk, I will first present the definition and some of the classical properties of Castelnuovo-Mumford regularity. Then we will turn to some known results and open questions on estimates for this invariant, when the base ring is a field. Next, we present a case where working over a more general base ring is very useful. Finally, if time permits, extensions of this notion to more general ones will be motivated and briefly described.
Updated on May 02, 2013 01:42 PM PDT
198. # Cherednik algebras and affine Lie algebras at negative level (NAGRT)

Location: MSRI: Simons Auditorium
Speakers: Eric Vasserot

We'll prove that the category O of some class of Cherednik algebras is equivalent to a highest weight subcategory of the (parabolic) category O of affine gl_n. This implies, in particular, some conjectural Kazhdan-Lusztig type character formulas for the simple modules. The proof uses categorifications and highest weight theory. This is a joint work with R. Rouier, P. Shan and M. Varagnolo.
Updated on Mar 22, 2013 05:29 AM PDT
199. # Cartier Crystals (COMMA)

Location: MSRI: Simons Auditorium
Speakers: Manuel Blickle (Johannes Gutenberg-Universität Mainz)

In joint work with Gebhard Böckle, we systematically study modules with a right action of Frobenius.
Up to nilpotent actions, the resulting category of Cartier Crystals satisfies some surprising and very strong finiteness conditions. The theory has connections to questions in commutative algebra (finiteness of local cohomology), birational geometry (test ideals) and number theory (constructible p-torsion sheaves, L-functions). In my talk I will explain the key features of the theory via simple examples, elaborate its connection with Grothendieck-Serre duality and discuss some of the aforementioned applications.
Updated on May 24, 2013 02:07 PM PDT
200. # Constructing modules with prescribed cohomology (COMMA)

Location: MSRI: Baker Board Room

Reverse homological algebra deals with questions like the following ones, concerning a ring $R$ and a (left) $R$-module $k$: What $Ext_R(k,k)$-modules have the form $\mathrm{Ext}_R(M,k)$ for some $R$-module $M$? What are the essential images of the functor $\mathrm{RHom}_R(?,k)$ from various subcategories of the derived category of $R$-modules to the derived category of DG modules over $\mathrm{RHom}_R(k,k)$?

Some answers to the second question will be presented when $R$ is commutative, noetherian and local and $k$ is its residue field.
Under an additional hypothesis on $R$, which holds for complete intersections and for Golod rings, the first question will be answered "up to truncations." A crucial step of the proof involves a contravariant Koszul duality for (not necessarily commutative) connected DG algebras.

Part of the talk is based on joint work with David Jorgensen.
Updated on Mar 22, 2013 07:58 AM PDT
201. # A-infinity structures associated with curves (NAGRT)

Location: MSRI: Simons Auditorium
Speakers: Alexander Polishchuk (University of Oregon)

The talk is based on my joint work with Robert Fisette.
We consider the A-infinity algebra associated with a certain generator of the derived category of coherent sheaves on a smooth projective curve. In the case of an elliptic curve this A-infinity algebra can be computed explicitly, and in particular, one can recover the j-invariant by looking at the higher products m_6 and m_8. In the higher genus curve we prove that the A-infinity structure can be uniquely recovered up to homotopy from the higher products up to m_6. We also study the map from the moduli space of curves with marked points given by the products m_3.
Updated on May 01, 2013 02:56 PM PDT
202. # Categorification (NAGRT)

Location: MSRI: Baker Board Room
Speakers: Catharina Stroppel (Hausdorff Research Institute for Mathematics, University of Bonn)

Updated on Nov 26, 2013 03:46 PM PST
203. # Semisimple Hopf actions on commutative domains (NAGRT)

Location: MSRI: Baker Board Room
Speakers: Chelsea Walton (Massachusetts Institute of Technology)

Let H be a semisimple (so, finite dimensional) Hopf algebra over an algebraically closed field k of characteristic zero and let A be a commutative domain over k. We show that if H acts on A \\'inner-faithfully\\', then H must be a group algebra. This answers a question of E. Kirkman and J. Kuzmanovich and partially answers a question of M. Cohen. This result also extends to working over k of positive characteristic. We also discuss results on Hopf actions on Weyl algebras as a consequence of the main theorem. This is joint work with Pavel Etingof.
Updated on May 24, 2013 11:22 AM PDT
204. # Test Ideals of Non-principal Ideals (COMMA)

Location: MSRI: Baker Board Room
Speakers: Kevin Tucker (Princeton University)

Test ideals are a measure of singularities in positive characteristic, and are analogs of multiplier ideals from characteristic zero. In this talk, I will describe some recent joint work with Karl Schwede on the test ideals of non-principal ideals. In particular, time permitting I will discuss a description of test ideals using regular alterations, as well as positive characteristic global division theorem for test ideals.
Updated on May 24, 2013 11:35 AM PDT
205. # Landau-Ginzburg/CFT correspondence via Temperley-Lieb categories (Matrix Factorization Day)

Location: MSRI: Baker Board Room
Speakers: Ana Ros Camacho

We present some recent progress on the LG/CFT correspondence which relates certain representations of the bosonic part of the vertex operator superalgebra for the N=2 minimal model and subcategories of permutation type matrix factorizations. Joint work with Alexei Davydov and Ingo Runkel.
Updated on Mar 15, 2013 06:09 AM PDT
206. # Matrix Factorizations in Knot Theory (Matrix Factorization Day)

Location: MSRI: Baker Board Room
Speakers: Hanno Becker

I begin by reviewing the original construction of Khovanov-Rozansky knot invariant based on tensor products of matrix factorizations. I will then explain how techniques from homotopical algebra apply to show that it can also be described in terms of stable Hochschild homology of Soergel bimodules; the latter are prominent in representation theory and also occur in the construction of other knot invariants. The description and techniques also allow for an alternative proof of the fact that one gets a knot invariant.
Created on Mar 15, 2013 05:13 AM PDT
207. # Orbifold completion of defect bicategories (Matrix Factorization Day)

Location: MSRI: Baker Board Room
Speakers: Nils Carqueville

Motivated by topological quantum field theory, one can start from any pivotal bicategory B and construct its "orbifold completion" B_orb in terms of certain Frobenius algebras. The completion satisfies the natural properties B \subset B_orb and (B_orb)_orb = B_orb, and it gives rise to various new equivalences and nondegeneracy results. I will explain this construction (which is joint work with Ingo Runkel) and apply it to the bicategory of isolated singularities and matrix factorisations. Applications include a unified perspective on ordinary equivariant matrix factorisations, a one-line proof of Knörrer periodicity, and new equivalences for simple singularities.
Created on Mar 15, 2013 05:12 AM PDT
208. # Orlov spectra: bounds and gaps (Matrix Factorization Day)

Location: MSRI: Baker Board Room
Speakers: Mathew Ballard

Created on Mar 15, 2013 05:10 AM PDT
209. # Morita theory of the affine Hecke category

Location: MSRI: Simons Auditorium
Speakers: David Nadler (University of California, Berkeley)

One can view the affine Hecke category of equivariant coherent sheaves on the Steinberg variety as a "matrix algebra" over the adjoint quotient of a reductive group. Thus one expects its center and abelianization (Hochschild cohomology and homology categories) to involve equivariant coherent sheaves on the commuting variety. We will present precise descriptions involving coherent sheaves with prescribed singular support. This is joint work with D. Ben-Zvi (Texas) and A. Preygel (Berkeley).
Updated on Nov 25, 2013 04:51 PM PST
210. # Hochschild homology, Grothendieck duality, and Brown representability (COMMA)

Location: MSRI: Simons Auditorium
Speakers: Amnon Neeman (Australian National University)

In a 2008 paper, Avramov and Iyengar studied Cohen-Macaulay and Gorenstein morphisms and characterized them in terms of invariants from Hochschild(co)homology.
The invariants in question turned out to be related to Grothendieck duality, and in a 2010 paper Avramov, Iyengar, Lipman and Nayak pursued the ideas to prove reduction formulas for the Hochschild (co)homology groups in question. In this talk, we will discuss a new approach to the problem, based on Brown representability.
Updated on May 17, 2013 04:46 PM PDT
211. # Categorification (NAGRT)

Location: MSRI: Baker Board Room
Speakers: Catharina Stroppel (Hausdorff Research Institute for Mathematics, University of Bonn)

Updated on Nov 26, 2013 03:46 PM PST
212. # Local cohomology of modules of covariants

Location: MSRI: Baker Board Room
Speakers: Michel van den Bergh (Limburgs Universitair Centrum)

There is an old conjecture by Stanley which gives a numerical
criterion for a module of covariants to be Cohen-Macaulay.
To prove this conjecture one has to be able to compute, or
at least estimate the local cohomology with support in the nullcone,
a question that has regained interest recently. For this reason I will
discuss my old work on this in which I give a precise (but complicated)
formula for the local cohomology with support in the nullcone as a
G-equivariant D-module, under some reasonably generic conditions.
Updated on May 23, 2013 02:59 PM PDT
213. # Commutative Algebra and Algebraic Geometry (Eisenbud Seminar)

Location: UC Berkeley

Commutative Algebra and Algebraic Geometry Seminar Tuesdays, 3:45-6:00 939 Evans Hall Organizer: David Eisenbud http://hosted.msri.org/alg/ 3:45 PM
F-singularities in families
Speaker: Wenliang Zhang

F-singularities are classes of singularities defined via the Frobenius endomorphism in characteristic p. One prominent method to measure these singularities is to introduce ideals that define the loci, such as the test ideal (a characteristic p analog of the multiplier ideal). However, these ideals may behave quite differently from their characteristic 0 counterparts. For instance, the test ideal may fail to satisfy the generic restriction theorem that holds for the multiplier ideal. This prompts a natural question, how do we study F-singularities in families?

In this talk, I will discuss recent joint work with Zsolt Patakfalvi and Karl Schwede on the behavior of F-singularities in families. In particular, I will discuss a relative version of the ideals mentioned in the previous paragraph and some restriction theorems for them. If time permits, some global geometric consequences will also be discussed.

5:00 PM
Periodicity of betti numbers of monomial curves.
Speaker: Vu Thanh

Let $k$ be an arbitrary field. Let $S = (a_1< ... Updated on Mar 18, 2013 03:40 AM PDT 214. # Geometry of Hurwitz Spaces Location: UC Berkeley, 60 Evans Hall Speakers: Joe Harris Riemann surfaces, which we now think of abstractly as smooth algebraic curves over the complex numbers, were described by Riemann as graphs of multivalued holomorphic functions-in other words, branched covers of the Riemann sphere$\P^1$. The Hurwitz spaces, varieties parametrizing the set of branched covers of$\P^1$of given degree and genus, are still central objects in the study of curves and their moduli. In this talk, we'll describe the geometry of Hurwitz spaces and their compactifications, leading up to recent work of Anand Patel and others. Updated on Mar 18, 2013 05:18 AM PDT 215. # Modules over deformation quantization (NAGRT) Location: MSRI: Simons Auditorium Speakers: Jeremy Pecharich (Pomona College) Let X be a holomorphic symplectic variety and F a coherent sheaf on X. Then a natural question to ask is if we take a deformation quantization of X can we also quantize the coherent sheaf F? We give an answer to this question, up to order 2, when the coherent sheaf is a direct image of a vector bundle supported on a smooth subvariety. If time permits we will also construct BV differentials on Tor and Ext groups between modules which admit quantizations. This is joint work with V.Baranovsky and V. Ginzburg. Updated on May 16, 2013 03:34 PM PDT 216. # Free divisors: examples and conjectures (COMMA) Location: MSRI: Simons Auditorium Speakers: Eleonore Faber (University of Toronto) Free divisors are certain non-normal hypersurfaces in a complex manifold, whose singular loci have nice algebraic properties: the Jacobian ideals are Maximal Cohen Macaulay modules for the hypersurface rings. In this talk we give a short introduction to free divisors, also to their original definition (due to K. Saito) via logarithmic derivations and logarithmic differential forms, and indicate in which areas of mathematics they appear. Then we talk about a conjecture about the singularities of some well-known free divisors, namely, normal crossing divisors. Finally we move on to logarithmic residues, a recent topic of interest, and to a conjecture about relationship between the logarithmic residue and the normalization of a free divisor. Updated on Jul 28, 2013 05:54 AM PDT 217. # Existence of good ideals in 2-dimensional normal Gorenstein rings (COMMA) Location: MSRI: Simons Auditorium Speakers: Kei-ichi Watanabe (Nihon University) Let (A,m) be a Noetherian Gorenstein local ring of dimension d. An m-primary ideal of A is called "good" if G(I):=\oplus I^n/I^{n+1} is Gorenstein with a(G) =1-d. Equivalently, if Q is a minimal reduction of I, I is good if and only if I^2=QI and Q:I = I. In a paper Goto-Iai-Watanabe, Good ideals in Gorenstein local rings, T.A.M.S. 353 (2000), we studied good ideals in 2 dimensional rational singularities. In this talk, we show existence of good ideals for non-rational surface singularities using cohomology groups of anti-nef cycles on a resolution of the singularity. This is a joint work with Tomohiro Okuma and Ken-ichi Yoshida. Updated on May 10, 2013 12:33 PM PDT 218. # Conformal field theory in a nutshell (COMMA) Location: MSRI: Baker Board Room Speakers: Ana Ros Camacho Updated on Mar 08, 2013 01:59 AM PST 219. # The Poincare series of modules over generic Gorenstein Artinian algebras (COMMA) Location: MSRI: Simons Auditorium Speakers: Liana Sega The Poincare series of a finitely generated module over a commutative local ring is defined to be the generating series of its Betti numbers. Although examples of rings with transcendental Poincare series exist, there seems to be an abundance of rings for which the Poincare series of all finitely generated modules are rational, sharing a common denominator. I will present recent work with Marilina Rossi, in which we prove that this property holds for generic Gorenstein Artinian algebras. When the socle degree is different than 3, this property holds more generally, for all local Artinian rings whose associated graded algebra is Gorenstein and has extremal (compressed) Hilbert series. Updated on Mar 08, 2013 02:02 AM PST 220. # Syzygies and Representation Theory (COMMA) Location: MSRI: Baker Board Room Speakers: Jerzy Weyman (Northeastern University) I will speak on the work of Enright-Hunziker and Pruett on resolutions of determinantal varieties. Updated on May 24, 2013 12:38 PM PDT 221. # Commutative Algebra and Algebraic Geometry (Eisenbud Seminar) Location: UC Berkeley Commutative Algebra and Algebraic Geometry Tuesdays, 3:45-6pm in Evans 939 organizer: David Eisenbud http://hosted.msri.org/alg 3:45 PM Algebra structures on short free resolutions Speaker: Lars Christensen Let$R$be a quotient of a regular local ring$Q$. If the free resolution of$R$over$Q$has length$2$, then its structure is given by the Hilbert--Burch Theorem. For longer resolutions the structure is significantly harder to describe, but for resolutions of length$3$a partial classification is available. I will discuss some recent progress, achieved in collaboration with Oana Veliche and Jerzy Weyman, towards completion of this classification. 5:00 PM The Golod Property for Monomial Ideals Speaker: David Berlekamp The Golod property for monomial ideals is implied by a simple criterion on GCD's. This can be used to prove that the product of any two monomial ideals is Golod. Updated on Mar 08, 2013 01:42 AM PST 222. # Coxeter groups, path algebras and preprojective algebras (NAGRT) Location: MSRI: Simons Auditorium Speakers: Idun Reiten To a finite acyclic quiver we can associate a path algebra kQ (k a field), a preprojective algebra and a Coxeter group. Using a natural map from the Coxeter group to ideals in the preprojective algebra,investigated in work with Buan, Iyama and Scott, we establish a 1-1 correspondence between elements in the Coxeter group and cofinite quotient closed subcategories of the finite dimensional kQ-modules. This is based on work with Oppermann and Thomas. Updated on Mar 08, 2013 02:01 AM PST 223. # Matrix factorizations of higher codimension (COMMA) Location: MSRI: Simons Auditorium Speakers: David Eisenbud (MSRI - Mathematical Sciences Research Institute) Updated on Dec 09, 2013 09:16 AM PST 224. # Modules for elementary abelian groups and vector bundles on projective space Location: UC Berkeley, 60 Evans Hall Speakers: David Benson (University of Aberdeen) I shall begin with a gentle introduction to modular representation theory of finite groups. Many questions about these reduce to the case of an elementary abelian p-group, so I shall spend most of the talk on these. In particular, I shall talk about modules of constant Jordan type, and what they have to do with algebraic vector bundles on projective space. Updated on May 24, 2013 10:08 AM PDT 225. # COMMA Focus Area Seminar Location: MSRI: Simons Auditorium Updated on Dec 19, 2012 02:50 AM PST 226. # Categorification Location: MSRI: Baker Board Room Speakers: Catharina Stroppel (Hausdorff Research Institute for Mathematics, University of Bonn) Updated on Nov 26, 2013 03:46 PM PST 227. # Noncommutative ruled surfaces Location: MSRI: Simons Auditorium Speakers: Kenneth Chan (University of Washington) The noncommutative minimal model program (ncMMP) uses the techniques of Mori theory to classify noncommutative surfaces, which we assume to be finite over their centres. The main result is a very pleasing analogy with the commutative theory - a noncommutative surface is either birational to a unique minimal model, or a noncommutative ruled surface. In this talk, I will explain how to associate a Brauer pair to a noncommutative surface, and how to run the ncMMP for these Brauer pairs. Although this is similar in spirit to the log MMP, there are some differences. Noncommutative ruled surfaces arise naturally in this context, and we will conclude with some structural results about them obtained by moduli theory. Updated on May 24, 2013 12:22 PM PDT 228. # Separating invariants and finite reflection groups Location: MSRI: Simons Auditorium Speakers: Emilie Dufresne (MSRI - Mathematical Sciences Research Institute) The study of separating invariants is a new trend in Invariant Theory and a return to its roots: invariants as a classification tool. Rather than considering the whole ring of invariants, one considers a separating set, that is, a set of invariants whose elements separate any two points which can be separated by invariants. In this talk, we focus on representations of finite groups. We show that if there exists a polynomial separating algebra, the the group action must be generated by (pseudo-)reflections. This produces a new, simpler proof of the classical result of Serre that if the ring of invariants is polynomial then the group action must be generated by (pseudo-)reflections. Updated on May 24, 2013 12:12 PM PDT 229. # limits of graded families of ideals Location: MSRI: Simons Auditorium Speakers: Steven Cutkosky (University of Missouri) Under very general conditions, asymptotic limits of graded families of ideals can be be computed by associating a cone generated by a corresponding integral semigroup and then taking the volume of an appropriate slice. We discuss this method, its origins, and its application to problems in commutative algebra. Updated on May 13, 2013 04:20 PM PDT 230. # Skew Calabi-Yau algebras and homological identities Location: MSRI: Simons Auditorium Speakers: Daniel Rogalski (University of California) A skew Calabi-Yau algebra A is a generalization of a Calabi-Yau algebra which allows for a non-trivial Nakayama automorphism. We develop formulas for the Nakayama automorphisms of other algebras derived from A by important constructions: (1) smash product algebras A#H for a Hopf algebras H acting on A, and (2) graded twists of A. We discuss applications of these formulas and open questions. This is joint work with Manny Reyes and James Zhang. Updated on Sep 11, 2013 03:32 PM PDT 231. # Bernstein-Sato polynomials, Jacobian ideals, and logarithmic vector fields Location: MSRI: Simons Auditorium Speakers: Hans Walther (Purdue University) The Bernstein-Sato polynomial of a hypersurface is related to several concepts in commutative algebra. After an introduction to the general properties of this polynomial, we will focus on the case of hyperplane arrangements. We will discuss relations to Milnor fibers, to the intersection lattice of the arrangement, and the Jacobian ideal of the arrangement. We will also discuss new results, in the arrangement case, on the conjectured connection between the topological zeta function and the Bernstein-Sato polynomial. Updated on May 28, 2013 08:06 AM PDT 232. # Syzygies and Representation Theory: Resolution of length three, part 2 Location: MSRI: Baker Board Room Speakers: Jerzy Weyman (Northeastern University) I will conclude speaking on resolutions of length 3 and Kac-Moody Lie algebras. Updated on May 24, 2013 12:38 PM PDT 233. # Commutative Algebra and Algebraic Geometry (Eisenbud Seminar) Location: UC Berkeley Speakers: Marti Lahoz Commutative Algebra and Algebraic Geometry Seminar Tuesdays, 3:45-6:00 939 Evans Hall Organized by David Eisenbud More information at http://hosted.msri.org/alg/ 3:45PM: Symmetric tensors, rank versus cactus rank. Kristian Ranestad The cactus rank of a form is the minimal length of an apolar subscheme to the form, and has therefore also been called the scheme length of the form. It is in general smaller than the rank, but its value for a general form is not known. We shall relate it to the dimension of the family of polynomials with given dimension for the space of partials of all orders. I shall report on recent results in work with Bernardi and Marques. 5:00PM: Maximal Cohen-Macaulay modules over cubic hypersurface rings of dimension 4 and 5 Marti Lahoz In this talk, I will give a new construction of stable Arithmetically Cohen-Macaulay (ACM) bundles on cubic hypersurfaces in$P^{4}$and$P^{5}$Our construction relies on the interpretation of MCM modules as objects in the derived category of modules over the even part of the Clifford algebra associated to a quadric fibration. If time permits, I will explain how choices in the threefold case induce different compactifications of the moduli space of Ulrich bundles of rank 2. This is a joint work with Emanuele Macrì and Paolo Stellari. Updated on May 01, 2013 05:05 PM PDT 234. # Tensor Ideals and Varieties for Modules Location: MSRI: Simons Auditorium Speakers: Sarah Witherspoon (Texas A & M University) We will introduce the theory of varieties for modules and tensor ideals in categories of modules of a Hopf algebra. We will describe a classification of (thick) tensor ideals for a class of Hopf algebras: the quantum elementary abelian groups. This is joint work with Julia Pevtsova. Updated on May 24, 2013 09:50 AM PDT 235. # Kn{\o}rrer periodicity and finite MF representation type Location: MSRI: Baker Board Room Speakers: Graham Leuschke (Syracuse University) Updated on Aug 12, 2013 08:15 AM PDT 236. # Matrix factorizations and topological field theory Location: MSRI: Simons Auditorium Speakers: Daniel Murfet (University of California, Los Angeles) Updated on May 24, 2013 11:13 AM PDT 237. # Categorification - Commons Room Speakers: Michael Ehrig Categorization Seminar 1:30 - 3:30 PM Commons Room Organizer: Catharina Stroppel Speaker: Michael Ehrig Updated on May 06, 2013 11:58 AM PDT 238. # Splittings for Rings of Modular Invariants Location: MSRI: Simons Auditorium Speakers: Jack Jeffries (University of Utah) Rings of polynomial invariants of finite group actions are among the most classical objects in commutative algebra. There are many beautiful theorems ensuring that the invariant ring has good properties when the order of group is invertible, but if the order of the group is not a unit (i.e., is divisible by the characteristic of the ground field), many of these properties become more subtle. One key issue is that the ring of invariants may fail to be a direct summand of the polynomial ring. In this talk, we will review some of these subtleties, and provide a generalization of a result of Singh on this direct summand property for rings of modular invariants. Updated on May 17, 2013 10:31 AM PDT 239. # Informal seminar on matrix factorizations Location: MSRI: Simons Auditorium Speakers: Juergen Herzog, Bernd Ulrich (Purdue University) Updated on May 28, 2013 10:20 AM PDT 240. # On the rank and decompositions of symmetric tensors Location: MSRI: Simons Auditorium Speakers: Kristian Ranestad Starting with quadrics I shall discuss old and more recent results on the variety of powersum decompositions of a form and related results and open problems on apolar subschemes of minimal length. Updated on May 01, 2013 05:05 PM PDT 241. # Syzygies and Representation Theory: Resolution of length three, part 1 Location: MSRI: Simons Auditorium Speakers: Jerzy Weyman (Northeastern University) I start the series of talks on the connection of resolutions of length 3 and Kac-Moody Lie algebras. In the first part I will discuss the background, definitions and older results. Updated on May 24, 2013 12:38 PM PDT 242. # Commutative Algebra and Algebraic Geometry (Eisenbud Seminar) Location: UC Berkeley Speakers: Laurent Gruson, Frank Sottile (Texas A & M University) Commutative Algebra and Algebraic Geometry Tuesdays, 3:45-6pm in Evans 939 Organizer: David Eisenbud http://hosted.msri.org/alg Date: Feb 26 3:45 A model of the moduli space of marked cubic surfaces Speaker: Laurent Gruson It is well known that the restricted Picard group$Pic_0(S)$of a cubic surface$S$in$P_3$is isomorphic to the root lattice$E_6$. The choice of such an isomorphism is a markng of the surface. The moduli space of marked cubic surfaces is thus acted on by the Weyl group$W(E_6)$. We seek a equivariant morphism of this moduli space into$P(E_6 \otimes C)$. Ellingsrud and Peskine have identified$Pic_0(S)\otimes C$with the vector space W of dual quadrics apolar" to S. Our morphism transforms$S$into the hyperplane of$W$consisting of quadrics containing the faces of the Sylvester pentahedron of$S$. We give an explicit form of this parametrization. 5:00 Symmetric output feedback control and isotropic Schubert calculus Speaker: Frank Sottile One area of application of algebraic geometry has been in the theory of the control of linear systems. In a very precise way, a system of linear differential equations corresponds to a rational curve on a Grassmannian. Many fundamental questions about the output feedback control of such systems have been answered by appealing to the geometry of Grassmann manifolds. This includes work of Hermann, Martin, Brockett, and Byrnes. Helmke, Rosenthal, and Wang initiated the extension of this to linear systems with structure corresponding to symmetric matrices, showing that for static feedback it is the geometry of the Lagrangian Grassmannian which is relevant. In my talk, I will explain this relation between geometry and systems theory, and give an extension of the work of Helmke, et al. to linear systems with skew-symmetric structure. For static feedback, it is the geometry of spinor varieties which is relevant, and for dynamic feedback it is quantum cohomology and orbifold quantum cohomology of Lagrangian and orthogonal Grassmannians. This is joint work with Chris Hillar. Updated on May 24, 2013 11:03 AM PDT 243. # Noncommutative Unique Factorization in Quantum Algebras Location: MSRI: Simons Auditorium Speakers: Kenneth Goodearl (University of California, Santa Barbara) Launois, Lenagan and Rigal proved that many generic quantized coordinate rings and quantum algebras are noncommutative UFDs in the sense introduced by Chatters and Jordan. Other ncUFDs and near UFDs" (in which all but finitely many height 1 prime ideals are principal) have appeared in recent joint work with K. Brown. We shall describe these results and relations with the problem of determining the Zariski topology on prime spectra of quantum algebras. Updated on Sep 06, 2013 02:17 PM PDT 244. # An Introduction to Noncommutative Algebraic Geometry Location: UC Berkeley, 60 Evans Hall Speakers: Toby Stafford (University of Manchester) In recent years a surprising number of insights and results in noncommutative algebra have been obtained by using the global techniques of projective algebraic geometry. Many of the most striking results arise by mimicking the commutative approach: classify curves, then surfaces, and we will use this approach here. As we will discuss, the noncommutative analogues of (commutative) curves are well understood while the study of noncommutative surfaces is on-going. In the study of these objects a number of intriguing examples and significant techniques have been developed that are very useful elsewhere. In this talk I will discuss several of them. Updated on May 24, 2013 11:18 AM PDT 245. # Invariants and separating morphisms Location: MSRI: Simons Auditorium Speakers: Emilie Dufresne (MSRI - Mathematical Sciences Research Institute) We study the invariants of an algebraic group action on an affine variety via separating morphisms, that is, dominant G-invariant morphism to another affine variety such that points which are separated by some invariant have distinct image. This is a more geometric take on the study of separating invariants, a new trend in invariant theory initiated by Derksen and Kemper. In this talk, I will discuss some results which indicate that the fact that the invariants are not always finitely generated is less significant than the fact that what we would want to call the quotient morphism is not always surjective. (Joint work with Hanspeter Kraft) Updated on May 24, 2013 12:12 PM PDT 246. # Similarities between algebra and topology across characteristics. Location: MSRI: Simons Auditorium Speakers: Theodore Stadnik This will be a survey talk focused on providing important and understandable examples. We will investigate the relationships among differential operators, topology, and algebraic geometry/commutative algebra as the characteristic of the base field changes from 0 to p > 0. Updated on May 23, 2013 09:23 AM PDT 247. # Singularity categories of small categories Location: MSRI: Simons Auditorium Speakers: Gregory Stevenson (Universität Bielefeld) I'll explain a sufficient condition on a small category for its category of representations to be Gorenstein in an appropriate sense. I then want to discuss the problem of finding generators for singularity categories of such categories of representations. More specifically, I'll talk around the idea of using the intrinsic structure of the small category to characterize the representations (over a regular ring) of finite projective dimension. Updated on May 23, 2013 12:37 PM PDT 248. # Studying local cohomology modules using invariant theory Location: MSRI: Simons Auditorium Speakers: Emily Witt (University of Minnesota Twin Cities) Consider a linearly reductive group acting nicely on a polynomial ring over a field of characteristic zero. This action endows an extra structure upon certain local cohomology modules of the ring; studying this structure has the potential to provide examples and answer open questions on local cohomology modules. We will present this theory through the example of local cohomology with support in the ideal generated by the maximal minors of a generic matrix; we will also mention how this theory can be applied in other settings (as part of work in progress). Updated on May 24, 2013 11:07 AM PDT 249. # A vanishing theorem for D-modules, and applications to t-structures for quantized symplectic varieties Location: MSRI: Simons Auditorium Speakers: Thomas Nevins The representation theory of many interesting algebras, including various kinds of Cherednik algebras, can be approached via equivariant D-modules: more precisely, one can construct functors (of quantum Hamiltonian reduction'') from categories of equivariant D-modules to representations of the algebras. I'll describe an effective combinatorial criterion for such functors to vanish on certain equivariant D-modules---equivalently, for certain equivariant D-modules to have no nonzero group-invariant elements. I will also explain consequences of this vanishing criterion for natural t-structures on the derived categories of sheaves over quantum analogs of various interesting symplectic algebraic varieties. Most of the talk will be low-tech and will presume no prior familiarity with the terms mentioned above. This is joint work with Kevin McGerty. Updated on Feb 14, 2013 06:09 AM PST 250. # Modules of constant radical type and associated bundles Location: MSRI: Simons Auditorium Speakers: Jon Carlson (University of Georgia) This is a report on joint work with Eric Friedlander, Julia Pevtsova and sometimes Andrei Suslin. We introduce higher rank variations on the notion of$\pi$-points as defined by Friedlander and Pevtsova for representations of finite group schemes. Using this we can define module of constant r-radical and r-socle type. Such modules determine bundles over the Grassmannian associated to the higher rank$\pi$-points in the case that the group scheme is infinitesimal of height one. When the group scheme is an elementary abelian p-group, there is universal function for computing the kernel bundles as modules over the structure sheaf of the Grassmannian of r-planes in n space. These ideas also extend to various sorts of subalgebra of restricted p-Lie algebras. Updated on Feb 12, 2013 01:44 AM PST 251. # Syzygies and Representation Theory Seminar: Introduction to Vinberg representations Location: MSRI: Baker Board Room Speakers: Steven Sam (University of California, Berkeley), Jerzy Weyman (Northeastern University) Jerzy Weyman will continue on Vinberg Representations and Steven Sam will start on the paper by Enright, Hunziker and Pruett. Updated on May 24, 2013 12:38 PM PDT 252. # Commutative Algebra and Algebraic Geometry (Eisenbud Seminar) Location: UC Berkeley Speakers: Elina Robeva Commutative Algebra and Algebraic Geometry Tuesdays, 3:45-6pm in Evans 939 Organizer: David Eisenbud http://hosted.msri.org/alg Date: Tuesday, Feb 19 3:45 The cone of Betti tables over a rational normal curve Speaker: Steven Sam Recent work of Eisenbud and Schreyer describes all of the linear inequalities that are satisfied by the Betti tables of graded modules over polynomial rings. There has been interest in giving analogous descriptions for other graded rings. In recent work with Kummini, we consider the homogeneous coordinate ring of a rational normal curve and relate its cone of Betti tables to the corresponding cone for a polynomial ring in 2 variables. As in the case of polynomial rings, the extremal rays are given by "pure resolutions". I will explain the idea behind this work and give conjectures for other rings of finite Cohen-Macaulay representation type. 5:00 Robust Toric Ideals Speaker: Elina Robeva An ideal of$k[x_1,..,x_n]$is robust if it is minimally generated by a universal Gröbner basis. This rare property is shared by monomial ideals, ideals of maximal minors of generic matrices, and Lawrence ideals. In this talk we'll discuss recent attempts to classify robust toric ideals, including a complete description for ideals generated in degree two. Along the way there will be many examples, some conjectures, and plenty of counterexamples. This is joint work with Adam Boocher. Updated on May 23, 2013 12:44 PM PDT 253. # Derived representation schemes and non-commutative geometry Location: MSRI: Simons Auditorium Speakers: Yuri Berest If k is a field, the set of all representations of an associative k-algebra A on a finite-dimensional vector space V can be given the structure of an affine k-scheme, called the representation scheme Rep_V(A). According to a heuristic principle proposed by M.Kontsevich and A.Rosenberg, the family of schemes {Rep_V(A)} for a given non-commutative algebra A should be thought of as a substitute or approximation' for Spec(A)'. The idea is that every property or non-commutative geometric structure on A should naturally induce a corresponding geometric property or structure on Rep_V(A) for all V. This viewpoint provides a litmus test for proposed definitions of non-commutative analogues of classical geometric notions, and in recent years many interesting structures in non-commutative geometry have originated from this idea. In practice, however, if an associative algebra A possesses a property of geometric nature (for example, A is a NC complete intersection, Cohen-Macaulay, Calabi-Yau, etc.), it may happen that, for some V, the scheme Rep_V(A) fails to have a corresponding property in the usual algebro-geometric sense. The reason for this seems to be that the representation functor Rep_V is not exact' and should be replaced by its derived functor DRep_V (in the sense of non-abelian homological algebra). The higher homology of DRep_V(A), which we call representation homology, obstructs Rep_V(A) from having the desired property and thus measures the failure of the Kontsevich-Rosenberg approximation.' In this this talk, after reviewing the construction of DRep_V, we will present several results and a number of explicit examples confirming the above intuition. If time permits, we will also discuss other applications of representation homology, including its relation to Hochschild, cyclic homology and algebraic K-theory. Updated on Feb 19, 2013 01:26 AM PST 254. # Informal seminar on matrix factorizations Location: MSRI: Baker Board Room Speakers: Ragnar-Olaf Buchweitz (University of Toronto) Updated on Sep 18, 2013 02:29 PM PDT 255. # Multiplicities of graded families of ideals Location: UC Berkeley, 60 Evans Hall Speakers: Steven Cutkosky (University of Missouri) The multiplicity of a local ring R is its most fundamental invariant. For example, it tells us how singular the ring is. The multiplicity is computed from the limit as n goes to infinity of the length of R modulo the nth power of its maximal ideal. Many other multiplicity like invariants naturally occur in commutative algebra. We discuss a number of naturally occurring limits of this type, and show that in very general rings, such limits always exist. Updated on May 13, 2013 04:20 PM PDT 256. # Counting Moduli of Quiver Representations with Relations Location: UC Berkeley Speakers: Jiarui Fei 4:10 – 5:30 PM 891 Evans Hall Counting Moduli of Quiver Representations with Relations Speaker: Jiarui Fei Abstract: In this talk, I will explain how to count the rational points of the GIT quotients of quiver representations with relations. I will focus on two types of algebras – one is extended from a quiver Q, and the other is Dynkin A_2 tensored with Q. For both, explicit formulas will be given. For application in the quantum algebra, we study when they are polynomial-count. We follow the similar line as quiver without relations using the Hall algebra. However, algebraic manipulations in Hall algebra will be replaced by corresponding geometric constructions. You will see many examples. Updated on Jan 29, 2013 05:26 AM PST 257. # Behrend's function is constant on Hilb^n(C^3) Location: MSRI: Simons Auditorium Speakers: Andrew Morrison (ETH Zürich) We prove that Behrend's function is constant on Hilb^n(C^3). A calculation of motivic zeta functions shows the relevant Milnor fibers have zero Euler characteristic. As a corollary we see that Hilb^n(C^3) is generically reduced. Updated on May 24, 2013 12:11 PM PDT 258. # Secant and tangential varieties of Segre-Veronese varieties Location: MSRI: Simons Auditorium Speakers: Claudiu Raicu (Princeton University) I'll explain a method for computing the defining ideals of the secant and tangential varieties of Segre-Veronese varieties, and describe some connections to plethysm problems. Updated on May 24, 2013 09:51 AM PDT 259. # Beyond pure resolutions and vector bundles with supernatural cohomology: Complexes associated to triplets Location: MSRI: Baker Board Room Speakers: Gunnar Floystad Updated on Jan 29, 2013 04:11 AM PST 260. # Periodicity of Betti numbers of some semigroup rings Location: MSRI: Simons Auditorium Speakers: Hema Srinivasan (University of Missouri) Given a finite subset A of positive integers, let S(A) denote the induced semigroup ring. In other words, S(A) is the coordinate ring of the monomial curve parametrized by A. For a positive integer j, write A+(j) for the subset obtain by adding j to each element in A. In this talk, we will discuss the conjecture that the Betti numbers of the semigroup ring S(A+(j)) are eventually periodic in j. In particular, this conjecture implies that the first Betti number of S(A+(j)), which is the minimal number of equations defining the associated monomial curve, is eventually periodic in j and hence bounded for all j. Updated on May 13, 2013 02:32 PM PDT 261. # Syzygies and Representation Theory Seminar: Introduction to Vinberg representations Location: MSRI: Baker Board Room Speakers: Jerzy Weyman (Northeastern University) Updated on May 24, 2013 12:38 PM PDT 262. # Commutative Algebra and Algebraic Geometry (Eisenbud Seminar) Location: UC Berkeley Speakers: Gunnar Carlsson February 05, 2013 939 Evans Hall 3:45PM Spaces and varieties of barcodes Speaker: Gunnar Carlsson Persistence barcodes are very interesting and useful summaries of the shape of point cloud data sets. They can be used to understand individual data sets, or data sets whose objects themselves have shapes. The set of barcodes can be understood as a space in various ways, one as a metric space, the other as an (infinite dimensional) algebraic variety. We\'ll discuss these ideas and ask for input on more general situations. 5:00PM Uniform annihilation of Ext modules and generation of derived categories Speaker: Ryo Takahashi This talk is based on ongoing joint work with Srikanth Iyengar. Let R be a commutative noetherian ring. We call a nonzerodivisor x of R a uniform annihilator if there exists an integer n>0 such that x annihilates Ext_R^n(M,N) for all finitely generated R-modules M and N. It follows from a result of Hsin-Ju Wang that R possesses a uniform annihilator if R is a complete local domain containing a field with perfect residue field. In this talk, we consider how to proceed in the general case. We also relate it with strong generation of the bounded derived category of finitely generated R-modules in the sense of Bondal and Van den Bergh. Updated on Feb 01, 2013 08:26 AM PST 263. # Residues and Duality for Schemes and Stacks Location: MSRI: Simons Auditorium Speakers: Amnon Yekutieli Let K be a regular noetherian commutative ring. I will begin by explaining the theory of rigid residue complexes over essentially finite type K-algebras, that was developed by J. Zhang and myself several years ago. Then I will talk about the geometrization of this theory: rigid residue complexes over finite type K-schemes. An important feature is that the rigid residue complex over a scheme X is a quasi-coherent sheaf in the etale topology of X. For any map f : X → Y between K-schemes there is a rigid trace homomorphism (that usually does not commute with the differentials). When the map f is proper, the rigid trace does commute with the differentials (this is the Residue Theorem), and it induces Grothendieck Duality. Then I will move to finite type Deligne-Mumford K-stacks. Any such stack \X has a rigid residue complex on it, and for any map f : \X → \Y between stacks there is a rigid trace homomorphism. These facts are rather easy consequences of the corresponding facts for schemes, together with etale descent. I will finish with the Residue Theorem, which holds when the map f : \X → \Y is proper and coarsely schematic; and the Duality Theorem, which also requires the map f to be tame. If there is time I will outline the proofs. - Lecture notes are at http://www.math.bgu.ac.il/~amyekut/lectures/resid-stacks/notes.pdf Updated on Jan 31, 2013 01:16 AM PST 264. # (Quantum) fusion versus (quantum) intersection Location: UC Berkeley, 60 Evans Hall Speakers: Catharina Stroppel (Hausdorff Research Institute for Mathematics, University of Bonn) Intersection theory grew out of very basic questions like: "given four generic lines in \mathbb{P}^3 - how many lines intersect all four of them?" Questions like that are one of the simplest examples of an application of Schubert Calculus, a very important tool in combinatorial representation theory. It is used to describe cohomology rings, but also to construct categories which describe representation theoretic problems geometrically. It serves as the basis of more sophisticated methods of enumerative geometry, like Gromov-Witten theory and Quantum Cohomology. An amazing fact is that the same combinatorics also occurs when decomposing tensor products of representations of a semisimple complex Lie algebra. This talk will describe some of these basic ideas and use them to explain a connection between quantum fusion products and quantum cohomology, relating Verlinde algebras and quantum cohomology rings. All this is related to questions arising in commutative and noncommutative algebraic geometry, integrable systems, representation theory, combinatorics ... Updated on Nov 26, 2013 03:46 PM PST 265. # Koszul homology of ideals generated by invariants and analogues of determinantal varieties Location: MSRI: Simons Auditorium Speakers: Jerzy Weyman (Northeastern University) Let$V$be a symplectic vector space of dimension$2n$. Given a partition$\lambda$with at most$n$parts, there is an associated irreducible representation$\bS_{[\lambda]}(V)$of$\Sp(V)$. This representation admits a resolution by a natural complex$L^{\lambda}_{\bullet}$, (called {\bf Littlewood complex}), whose terms are restrictions of representations of$\GL(V)$. When$\lambda$has more than$n$parts, the representation$\bS_{[\lambda]}(V)$is not defined, but the Littlewood complex$L^{\lambda}_{\bullet}$still makes sense. I will explain how to compute its homology. One finds that either$L^{\lambda}_{\bullet}$is acyclic or it has a unique non-zero homology group, which forms an irreducible representation of$\Sp(V)$. The non-zero homology group, if it exists, can be computed by a rule reminiscent of that occurring in the Borel--Weil--Bott theorem. This result categorifies earlier results of Koike--Terada on universal character rings. The result has an interpretation in terms of commutative algebra: it calculates the Koszul homology of the ideal generated by invariants of the symplectic group on the set of vectors. One can prove analogous results for orthogonal and general linear groups. If time permits I will show how some of these ideas can be generalized to exceptional groups. The talk is based on the joint paper with Andrew Snowden and Steven Sam and another one with Steven Sam. Updated on May 24, 2013 12:38 PM PDT 266. # Building Cohen-Macaulay modules from a single module Location: MSRI: Simons Auditorium Speakers: Ryo Takahashi This talk is based on joint work with Hailong Dao. Let R be a Cohen-Macaulay local ring. Recall that R is said to have finite CM-representation type if there are only finitely many isomorphism classes of indecomposable (maximal) Cohen-Macaulay R-modules. In this case, clearly there exists a finitely generated R-module M out of which all Cohen-Macaulay R-modules are built by taking direct sums and direct summands. The converse is also true, namely, such a module M does not exist if R has infinite CM-representation type. Now a natural question arises: what if we also allow taking syzygies and a fixed number of extensions? This is a main problem which we deal with in this talk Updated on Jan 11, 2013 12:47 AM PST 267. # 5-minute talks Location: MSRI: Simons Auditorium Updated on Jan 18, 2013 05:59 AM PST 268. # Galois groups of Schubert problems Location: MSRI: Simons Auditorium Speakers: Frank Sottile (Texas A & M University) Building on work of Jordan from 1870, in 1979 Harris showed that a geometric monodromy group associated to a problem in enumerative geometry is equal to the Galois group of an associated field extension. Vakil gave a geometric-combinatorial criterion that implies a Galois group contains the alternating group. With Brooks and Martin del Campo, we used Vakil's criterion to show that all Schubert problems involving lines have at least alternating Galois group. My talk will describe this background and sketch a current project to systematically determine Galois groups of all Schubert problems of moderate size on all small classical flag manifolds, investigating at least several million problems. This will use supercomputers employing several overlapping methods, including combinatorial criteria, symbolic computation, and numerical homotopy continuation, and require the development of new algorithms and software. Updated on May 24, 2013 11:03 AM PDT 269. # Ekedahl invariants for Finite Groups Location: MSRI: Simons Auditorium Speakers: Ivan Martino In 2009 T. Ekedahl introduced some cohomological invariants for a finite group G. These relate, naturally, to invariant theory for groups and, also, to the Noether's Problem (one wonders about the rationality of the extension F(G) = F(x_g: g in G)^G over F, for a field F and a finite group G). In this talk, we introduce these invariants and we highlight some results. Created on Dec 17, 2012 06:06 AM PST 270. # Hereditary Chip-Firing Ideals Location: MSRI: Simons Auditorium Speakers: Spencer Backman Chip-firig on graphs is a simple game with surprisingly deep connections to various parts of mathematics, and the lattice ideal of the Laplacian matrix of a graph encodes all of the combinatorics. We introduce a new family of subideals of the Laplacian lattice ideal with distinguished Gr"obner bases coming from generalized chip-firing dynamics on a graph as induced by abstract simplicial complexes on the vertex set. We will describe a conjecture generalizing a result of Postnikov and Shapiro relating the initial ideals of these binomial ideals to their power ideal deformations. Updated on Dec 04, 2012 01:18 AM PST 271. # Fock-Goncharov Reading Seminar Location: MSRI: Simons Auditorium Updated on Oct 19, 2012 03:09 AM PDT 272. # The generic initial ideal of a matroid. Location: MSRI: Simons Auditorium Speakers: Thomas Kahle We show that if a matroid is the truncation (=skeleton) of another matroid, then the generic initial ideal of its Stanley-Reisner ideal is level. In characteristic zero, the generic initial ideal is strongly stable and therefore admits an Artinian reduction by variables. Consequently the h-vectors of truncations of matroids satisfy Stanley's conjecture: They are Hilbert functions of Artinian monomial level algebras. This is joint work with Alexandru Constantinescu and Matteo Varbaro. Updated on Dec 07, 2012 03:34 AM PST 273. # Graded quiver varieties and quantum cluster algebras Location: MSRI: Simons Auditorium Speakers: Fan Qin For an acyclic quantum cluster algebra, we identify its generic quantum cluster characters with Nakajima's qt-characters defined via graded quiver varieties. As a consequence, we obtain the monoidal categorification conjecture in level 1 case. This talk is based on a joint-work with Yoshiyuki Kimura. Updated on Dec 07, 2012 03:33 AM PST 274. # Resolutions of monomial ideals using simplicial complexes Location: MSRI: Simons Auditorium Speakers: Sara Faridi Given a monomial ideal, Bayer, Peeva and Sturmfels expanded work of Taylor by providing a criterion for when a simplicial complex labeled by the generators of the ideal would support a free resolution of the ideal. In this talk we focus on the situation when the supporting complex is a simplicial tree, and discuss some related structures. Updated on Nov 30, 2012 01:44 AM PST 275. # Hall algebra and Counting Location: MSRI: Simons Auditorium Speakers: Jiarui Fei (University of California) In this talk, I will explain how simple-minded counting can lead to some interesting results about the cluster algebra. I use Hall algebra as a key organizing tool to make our counting an enjoyable experience. Updated on Dec 07, 2012 12:45 AM PST 276. # Toric varieties, higher duals and polytopes Location: MSRI: Simons Auditorium Speakers: Alicia Dickenstein (University of Buenos Aires) I will present joint work with several coauthors on the description of (higher) duals of (equivariantly embedded) toric varieties and the relation with the associated polytopes/lattice configurations. The interplay between algebraic geometry and combinatorics allows us to prove algebro-geometric statements with combinatorial tools and combinatorial statements with algebro-geometric tools. Updated on Sep 05, 2013 02:03 PM PDT 277. # Cluster Algebras Open Problem Session, Atrium Updated on Dec 07, 2012 12:44 AM PST 278. # The combinatorics of toric ideals of hypergraphs Location: MSRI: Simons Auditorium Speakers: Elizabeth Gross The edge subring of a hypergraph H is the monomial subalgebra parameterized by the hyperedges of H. Its defining ideal is a toric ideal which we can understand by studying the combinatorics of H. In this talk we will survey recent results on the toric ideals of hypergraphs with a particular focus on the combinatorics of minimal generators. Updated on Dec 07, 2012 06:35 AM PST 279. # When do monomial ideals have linear resolutions? Location: MSRI: Simons Auditorium Speakers: Emma Connon In 1990 Fröberg showed that the edge ideal of a graph has a linear resolution if and only if the complement of the graph is chordal. In this talk we will discuss the generalization of Fröberg's theorem to higher dimensions. In particular we will discuss new classes of simplicial complexes which extend the notion of a chordal graph and which give rise to a necessary condition for an ideal to have a linear resolution over any field. We will also provide a necessary and sufficient combinatorial condition for a square-free monomial ideal to have a linear resolution over fields of characteristic two. Updated on Dec 07, 2012 06:33 AM PST 280. # Logarithmic vector fields and curve configurations Location: MSRI: Simons Auditorium Speakers: Hal Schenck Let A be the union U(C_i) of a finite number of smooth plane curves C_i, such that the singular points of A are quasihomogeneous. This means that locally (at a singular point), the equation of A is homogeneous. We prove that if C is a smooth curve such that the singularities of A U C are quasihomogeneous, then there is a short exact sequence relating the bundle of logarithmic derivations on A to the bundle of logarithmic derivations on A U C. This yields an inductive tool for studying the splitting of these bundles in terms of the geometry of the divisor A|_C on C. (joint work with H. Terao and M. Yoshinaga, Hokkaido U.) Updated on May 01, 2013 04:48 PM PDT 281. # Joint MSRI/NRing: Women in Mathematics Lunch Location: MSRI: Baker Board Room Bring your own lunch. Updated on Nov 28, 2012 06:48 AM PST 282. # Construction of quantum clusters via noncommutative UFDs Location: MSRI: Baker Board Room Speakers: Milen Yakimov CGL (Cauchon-Goodearl-Letzter) extensions form a large, axiomatically defined class of iterated Ore extensions. Various important families, such as quantum Schubert cell algebras and quantum Weyl algebras, arise as special cases. From the point of view of noncommutative algebra, this is the "best" current definition of quantum nilpotent algebras. We will describe a general contruction of quantum clusters on all of these algebras via noncommutative unique factorization domains. The structure of their prime elements sees combinatorics that was previously specific to Weyl groups. Another aspect of this work is that quantum clusters are intrinsically constructed as unique families of prime elements of chains of subalgebras, while previous constructions relied on direct arguments with quantum minors. This is a joint work with Ken Goodearl (UC Santa Barbara). Updated on May 02, 2013 11:37 AM PDT 283. # Cluster Algebras Open Problem Session Location: MSRI: Baker Board Room Updated on Nov 27, 2012 01:10 AM PST 284. # Wonder of sine-Gordon Y-systems Location: MSRI: Baker Board Room Speakers: Tomoki Nakanishi The sine-Gordon Y-systems and the reduced sine-Gordon Y-systems were introduced by Roberto Tateo in 90\'s in the study of the integrable deformation of the minimal models in conformal field theory by the thermodynamic Bethe ansatz method. They are associated to continued fractions, and the periodicity property of these Y-systems was conjectured by Tateo; however, it has been only partially proved so far. We prove the periodicity in full generality using the surface method of cluster algebras. It turns out that there is a wonderful interplay among continued fractions, triangulations, cluster algebras, and Y-systems, which I would like to explain in this talk. This is a joint work with Salvatore Stella. Updated on Nov 27, 2012 01:23 AM PST 285. # The Positive Part of a Tropical Variety Location: MSRI: Simons Auditorium Speakers: Sarah Brodsky Updated on Nov 21, 2012 04:49 AM PST 286. # Examples of Frobenius splitting in combinatorial commutative algebra Location: MSRI: Simons Auditorium Speakers: Jenna Rajchgot (MSRI - Mathematical Sciences Research Institute) I'll review some of the basics of Frobenius splitting and explain how this theory has been used to study a number of varieties arising in combinatorial commutative algebra (eg. those discussed in part 3 of the Miller-Sturmfels textbook). The majority of this talk will be expository and no knowledge of Frobenius splitting will be assumed. Updated on Nov 21, 2012 06:59 AM PST 287. # Monoidal Categorification of cluster algebras. Location: MSRI: Simons Auditorium Speakers: Sarah Scherotzke I will give an overview of monoidal categorifications of Cluster algebras via Quantum groups and Nakajima quiver varieties. I will explain how these two approaches are connected. Updated on Nov 28, 2012 02:46 AM PST 288. # Box splines, polynomial interpolation, and zonotopal algebra Location: MSRI: Simons Auditorium Speakers: Olga Holtz I will discuss recent advances in zonotopal algebra, a subject that connects analysis problems on multivariate polynomial interpolation and box splines to problems of commutative algebra concerning special polynomial ideals to problems of combinatorics involving hyperplane arrangements and lattice points in zonotopes. Updated on Nov 29, 2012 04:56 AM PST 289. # Rigidity of quantum tori and description of automorphism groups Location: MSRI: Simons Auditorium Speakers: Milen Yakimov We will describe a general rigidity theorem for quantum tori. It leads to a scheme that can be used to classify the (full) automorphism groups of algebras that admit one quantum cluster (i.e. can be squeezed between a quantum affine space algebra and the corresponding quantum torus). The technique has a broad range of applications and in particular settles a couple of conjectures of Andruskiewitsch-Dumas and Launois-Lenagan. The former describes the automorphism groups of the algebras U_q^+(g) and the latter those of the algebras of square quantum matrices. Updated on May 02, 2013 11:37 AM PDT 290. # Ideals generated by 2-minors Location: MSRI: Simons Auditorium Speakers: Juergen Herzog Updated on May 01, 2013 05:02 PM PDT 291. # Cluster Algebras Open Problem Session, Atrium Updated on Nov 20, 2012 01:23 AM PST 292. # Commutative Algebra and Algebraic Geometry (Eisenbud Seminar) Location: UC Berkeley Speakers: Adam Boocher, Franz Winkler UC Berkeley Commutative Algebra and Algebraic Geometry Seminar November 27, 2012 939 Evans Hall 3:45PM: Algebraic ordinary differential equations: General rational solutions and classification Franz Winkler, Research Institute for Symbolic Computation (RISC) , J. Kepler University Linz, Austria Consider an algebraic ODE (AODE) of the form$F(x,y,y\\')=0$, where$F$is a tri-variate polynomial, and$y\\' = \frac{dy}{dx}$. The polynomial$F$defines an algebraic surface, which we assume to admit a rational parametrization. Based on such a parametrization we can generically determine the existence of a rational general solution, and, in the positive case, also compute one. This method depends crucially on curve and surface parametrization and the determination of rational invariant algebraic curves. Further research is directed towards a classification of AODEs w.r.t. groups of transformations (affine, birational) preserving rational solvability. 5:00PM: Golod Algebras Adam Boocher Updated on Nov 21, 2012 05:13 AM PST 293. # The Robbins phenomenon: cluster algebras and numerical p-adic arithmetic Location: MSRI: Simons Auditorium Speakers: Kiran S. Kedlaya In modern number theory, it is becoming increasingly common to make computer calculations using p-adic numbers. Just as for real numbers, this involves working with finite approximations and managing the resulting errors as they propagate through the computation. In general, the most flexible framework for this seems to be the natural p-adic analogue of floating-point arithmetic. David Robbins discovered an example of a computation in which errors in p-adic arithmetic do not appear to compound as is typical: the Dodgson (Lewis Carroll) condensation recurrence for computing determinants. Based on numerical evidence, he conjectured that the loss of p-adic accuracy during a p-adic floating point computation of the condensation recurrence is controlled by the maximum valuation of any denominator appearing in the computation (i.e., by the largest precision loss at a single step rather than the sum of these). Additional numerical evidence suggests that this conjecture should follow from a purely algebraic statement applicable to arbitrary cluster algebras. Using a power series deformation of the caterpillar lemma, we prove a weaker algebraic statement which implies a direct analogue of the Robbins conjecture for some simpler recurrences (Somos-4, Somos-5, Markoff). For a recurrence derived from a general cluster algebra, we obtain a weaker analogue of the Robbins conjecture in which the bound is multiplied by a small positive integer depending on the recurrence (e.g., 3 for condensation). Joint work with Joe Buhler (CCR La Jolla). Updated on Nov 20, 2012 01:19 AM PST 294. # Green's Hyperplane Restriction Theorem Location: MSRI: Simons Auditorium Speakers: Ornella Greco In this talk, we will give an introduction to Green's hyperplane restriction theorem, that gives a bound on the Hilbert function of the restriction of a symmetric algebra to a generic linear form. Moreover, we will talk about the generalization of this theorem to modules. Updated on Nov 21, 2012 05:26 AM PST 295. # Rees Algebras of Some Classes of Simplicial Complexes Location: MSRI: Simons Auditorium Speakers: Ali Alilooee In 1995, Villarreal gave a combinatorial description of the defining ideals of Rees algebras of quadratic square-free monomial ideals. In this paper we will generalize his results for hypergraphs. Our approach is based on giving a definition of closed even walks in a simplicial complex. We apply this combinatorial method to square-free monomial ideals of higher dimension. Updated on Nov 21, 2012 05:26 AM PST 296. # Tropical Moduli Spaces Location: MSRI: Baker Board Room Updated on Oct 18, 2012 11:07 AM PDT 297. # Quiver mutation and quantum dilogarithm identities Location: UC Berkeley, 60 Evans Hall Speakers: Bernhard Keller A quiver is an oriented graph. Quiver mutation is an elementary operation on quivers which appeared in physics in Seiberg duality in the 1990s and in mathematics in Fomin-Zelevinsky's definition of cluster algebras in 2002. In this talk, I will show how, by comparing sequences of quiver mutations, one can construct identities between products of quantum dilogarithm series. These identities generalize Faddeev-Kashaev-Volkov's classical pentagon identity and the identities obtained by Reineke. Morally, the new identities follow from Kontsevich-Soibelman's theory of Donaldson-Thomas invariants. They can be proved rigorously using the theory linking cluster algebras to quiver representations. Updated on Nov 16, 2012 02:29 AM PST 298. # Polytropes and Tropical Eigenspaces Location: UC Berkeley Speakers: Ngoc Tran The UC Berkeley Combinatorics Seminar Fall 2012, Monday 2:10pm - 3pm, Evans Hall 939, CCN 54496 939 Evans Hall Organizers: Florian Block, Max Glick, and Lauren Williams Title: Polytropes and Tropical Eigenspaces Speaker: Ngoc Tran Abstract: The map which takes a square matrix$A$to its polytrope is piecewise linear. We show that cones of linearity of this map form a fan partition of$\{R}^{n \times n}$, whose face lattice is anti-isomorphic to the lattice of complete set of connected relations. This fan refines the non-fan partition of$\R^{n \times n}$corresponding to cones of linearity of the eigenvector map. Our results answer open questions in a previous work with Sturmfels and lead to a new combinatorial classification of polytropes and tropical eigenspaces. Updated on Nov 21, 2012 05:01 AM PST 299. # Cohen-Macaulayness of large ordinary and symbolic powers of Stanley-Reisner ideals Location: MSRI: Simons Auditorium Speakers: Ngo Trung It is known that all ordinary powers of a Stanley-Reisner ideal I_D is Cohen-Macaylay if D is a complete intersection complex. Recently it was found that all symbolic powers of a Stanley-Reisner ideal I_D are Cohen-Macaulay if and only if D is a matroid complex. I will show how one can use tools of integer programming to prove this result. The next question is when a fixed ordinary or symbolic power of I_D is Cohen-Macaulay. For that I will present a characterization of complexes which are locally matroid or complete intersection complexes. From this it follows that if an ordinary or symbolic power of I_D is Cohen-Macaulay for some power greater than 2, then it will imply that D is a matroid or a complete intersection complex, respectively. Updated on May 09, 2013 10:26 AM PDT 300. # Cluster Algebras Open Topics Location: MSRI: Baker Board Room Updated on Nov 15, 2012 06:56 AM PST 301. # Commutative Algebra and Algebraic Geometry Seminar (Eisenbud Seminar) Location: UC Berkeley Speakers: Bernd Sturmfels (UC Berkeley Math Faculty), Seth Sullivant (North Carolina State University) Commutative Algebra and Algebraic Geometry Evans 939 Organizer: David Eisenbud http://hosted.msri.org/alg Date: Tuesday, November 20 3:45: Seth Sullivant, North Carolina State U: Algebraic Statistics Algebraic statistics advocates polynomial algebra as a tool for addressing problems in statistics and its applications. This connection is based on the fact that most statistical models are defined either parametrically or implicitly via polynomial equations. The idea is summarized by the phrase "Statistical models are semialgebraic sets". I will try to illustrate this idea with two examples, the first coming from the analysis of contingency tables, and the second arising in computational biology. I will keep the algebraic and statistical prerequisites to a minimum and keep the talk accessible to a broad audience. 5:00: Bernd Sturmfels, UC Berkeley: Commutative Algebra of Statistical Ranking A model for statistical ranking is a family of probability distributions whose states are orderings of a fixed finite set of items. We represent the orderings as maximal chains in a graded poset. The most widely used ranking models are parameterized by rational function in the model parameters, so they define algebraic varieties. We study these varieties from the perspective of combinatorial commutative algebra. One of our models, the Plackett-Luce model, is non-toric. Five others are toric: the Birkhoff model, the ascending model, the Csiszar model, the inversion model, and the Bradley-Terry model. For these models we examine the toric algebra, its lattice polytope, and its Markov basis. This is joint work with Volkmar Welker. Updated on Sep 13, 2013 10:26 AM PDT 302. # Triangular and tropical properties of dual canonical bases of quantum cluster algebras Location: MSRI: Simons Auditorium Speakers: Fan Qin Assume that a quantum cluster algebra admits a monoidal categorification by quantum affine algebras or quantum unipotent subgroups of simply-laced type. We show that, for any chosen cluster, the dual canonical basis is a triangular basis with respect to certain linearly independent set, and the basis elements are naturally parametrized by the extended g-vectors. Updated on Nov 15, 2012 06:57 AM PST 303. # j-multiplicity: A survey Location: MSRI: Simons Auditorium Speakers: Jonathan Montano (Purdue University) The j-multiplicity was introduced by Achiles and Manaresi in 1993 as a generalization of the Hilbert-Samuel multiplicity for arbitrary ideals in a Noetherian ring. Many of the properties and algebraic applications of the Hilbert-Samuel multiplicity of zero dimensional ideals have been extended to more general classes of ideals using the j-multiplicity. In this talk, I will review some of these properties and applications. At the end of the talk, I will briefly discuss my current research in this area. Updated on Nov 16, 2012 06:49 AM PST 304. # Splittings for Rings of Modular Invariants Location: MSRI: Simons Auditorium Speakers: Jack Jeffries (University of Utah) Rings of polynomial invariants of finite group actions are among the most classical objects in commutative algebra. There are many beautiful theorems ensuring that the invariant ring has good properties when the order of the group is invertible. However, if the order of the group is not a unit (i.e., is divisible by the characteristic of the ground field), many of these properties become more subtle. In this talk, I aim to illustrate some of the differences in invariant theory in this setting, and to describe some of my work in progress in this area. Updated on May 17, 2013 10:31 AM PDT 305. # Secant Varieties, Symbolic Powers, Statistical Models Location: UC Berkeley, 60 Evans Hall Speakers: Seth Sullivant The join of two algebraic varieties is obtained by taking the closure of the union of all lines spanned by pairs of points, one on each variety. The secant varieties of a variety are obtained by taking the iterated join of a variety with itself. The symbolic powers of ideals arise by looking at the equations that vanish to high order on varieties. Statistical models are families of probability distributions with special structures which are used to model relationships between collections of random variables. This talk will be an elementary introduction to these topics. I will explain the interrelations between these seemingly unrelated topics, in particular, how symbolic powers can shed light on equations for secant varieties, and how theoretical results on secant varieties shed light on properties of statistical models including mixture models and the factor analysis model. Particular emphasis will be placed on combinatorial aspects including connections to graph theory. Updated on Oct 19, 2012 02:31 AM PDT 306. # The UC Berkeley Combinatorics Seminar Location: UC Berkeley Speakers: Gregg Musiker (University of Minnesota Twin Cities) The UC Berkeley Combinatorics Seminar Mondays 2:10pm - 3:00pm 939 Evans Hall Organizers: Florian Block, Max Glick, and Lauren Williams Brane Tilings and Cluster Algebras: the dP3 lattice Speaker: Gregg Musiker Abstract: We discuss the link between cluster algebras and brane tilings and how this can be used to obtain combinatorial formulas for cluster variables arising from certain periodic quivers. No prior knowledge of brane tilings will be assumed. I will focus mostly on the case of the del Pezzo 3 (dP3) lattice and, in particular, work with Sicong Zhang at the 2012 REU at University of Minnesota. Connections to other examples such as Gale-Robinson sequences and Aztec Diamonds, including work with In-Jee Jeong from the 2011 REU, will also be discussed, time permitting. Updated on Sep 10, 2013 01:57 PM PDT 307. # On the computation of generalized Ehrhart series Location: MSRI: Simons Auditorium Speakers: Winfried Bruns (Universität Osnabrück) Let P be a rational polytope. The Ehrhart function counts the number of lattice points in kP for all natural numbers k. The corresponding ordinary generating function is called the Ehrhart series, and is well known to be the power series expansion of a rational function at the origin. From an abstract viewpoint counting of lattice points can be interpreted as integration of the constant 1 with respect to the counting measure defined by the lattice. We will discuss the generalization in which the constant 1 is replaced by a polynomial, and the generalized Ehrhart function is given by the assignment$k\mapsto \sum f(x)$where the sum is extended over the lattice points in kP. Our approach is based on Stanley decompositions and completely algorithmic. It has recently be implemented as a computer program. We will illustrate the computations by examples from combinatorial voting theory. Updated on Sep 18, 2013 02:22 PM PDT 308. # Fock-Goncharov Reading Seminar: Surfaces and Wall-Crossing Location: MSRI: Simons Auditorium Speakers: Harold Williams Updated on Nov 09, 2012 02:08 AM PST 309. # Matroids over rings Location: MSRI: Simons Auditorium Speakers: Alexander Fink A number of generalizations of matroids have been introduced, which contain more information than the purely linear-algebraic data that matroids do. Some examples are Dress and Wenzel's _valuated matroids_ and D'Adderio and Moci's _arithmetic matroids_. This talk is propaganda for a definition: I will introduce a notion of matroid over any commutative ring, of which the foregoing objects are special cases. In the Dedekind domain case, we can prove structure theorems and define the analogue of the Tutte polynomial. This is joint work with Luca Moci. Updated on Nov 07, 2012 11:39 AM PST 310. # c-vectors as dimension vectors Location: MSRI: Simons Auditorium Speakers: Alfredo Nájera Chávez In the theory of cluster algebras, a prominent role is played by a family of integer vectors called the c-vectors. In this talk, I will present a study of these vectors from the point of view of representations of quivers. In particular, we will see that positive c-vectors of skew-symmetric cluster algebras are always dimension vectors of indecomposable representations without self-extensions. Updated on Nov 12, 2012 12:34 AM PST 311. # Vector bundles on P^n and representations of GL_n Location: MSRI: Simons Auditorium Speakers: David Eisenbud (MSRI - Mathematical Sciences Research Institute) The description of cohomology tables in Boij-Soederberg theory can be thought of as saying that an arbitrary vector bundle on P^n "looks like" a certain homogeneous bundle (that is, one made from a representation of GL_n applied to the tangent bundle). I will explain this connection, and a new application of the philosophy that leads to sharp statements about the vanishing of cohomology of tensor products of bundles on P^n. This is all joint work with Frank Schreyer. Updated on Dec 09, 2013 09:16 AM PST 312. # Glicci ideals Location: MSRI: Simons Auditorium Speakers: Elisa Gorla Using complete intersections to link ideals is a classical technique, which can be traced back to Noether, Macaulay, and Severi among others. Although it started as a computational tool and a proof technique, liaison developed into a theory of independent interest. For ideals of height 3 or higher, one can consider liaison via Gorenstein ideals as a generalization of the classical liaison via complete intersection ideals of height 2. In this talk, we consider liaison via Gorenstein ideals. An ideal is called glicci if it can be linked to a complete intersection in a finite number of steps. A central question within Gorenstein liaison asks whether any Cohen-Macaulay ideal is glicci. I will introduce liaison and discuss this question, with an eye on the examples coming from determinantal ideals. Updated on Nov 09, 2012 02:11 AM PST 313. # Cluster Algebras Open Topics An informal meeting in the Atrium over lunch to discuss open topics. Updated on Nov 08, 2012 04:55 AM PST 314. # Commutative Algebra and Algebraic Geometry Seminar (Eisenbud Seminar) Location: UC Berkeley Speakers: Luke Oeding Commutative Algebra and Algebraic Geometry Evans 939 Organizer: David Eisenbud http://hosted.msri.org/alg Date: Tuesday, November 13 3:45: Luke Oeding (Berkeley): Eigenvectors of tensors and Waring decomposition Waring’s problem for polynomials is to write a given polynomial as a minimal sum of powers of linear forms. The minimal number of summands required in a Waring decomposition (the Waring rank) is related to secant varieties. I will explain recent work of Landsberg and Ottaviani that unified and generalized many constructions for equations of secant varieties via vector bundle techniques. With Ottaviani we have turned this construction into effective algorithms to actually find the Waring decomposition of a polynomial (provided the Waring rank is below a certain bound). Our algorithms generalize Sylvester’s algorithm for binary forms, using an essential new ingredient – eigenvectors of tensors. Of course a naive algorithm always exists, but is rarely effective. I will explain how computations using linear algebra make our algorithms effective. Given time, I will demonstrate our Macaulay2 implementations. 5:00: Grigory Mikhalkin: Tropical curves and their phases: from face to edge models We look at the constructions of embedded and immersed real algebraic curves in the plane. We survey and compare patchworking and tropical construction. As an example we consider topological classification of rational quintics in RP2. The first half of the talk will contain a short introduction to tropical curves and their phases. Updated on Sep 10, 2013 12:31 PM PDT 315. # Asymptotic triangulations Location: MSRI: Simons Auditorium Speakers: Karin Baur We introduce the notion of asymptotic triangulations of the annulus. We study their behaviour under mutation and describe their exchange graphs. Joint work with Gregoire Dupont. Updated on Nov 08, 2012 04:53 AM PST 316. # Regularity of associated graded modules in dimension one Location: MSRI: Simons Auditorium Speakers: Justin Chen Following a recent paper by Dung (arXiv: 1209.3469v1), a (sharp) bound for the regularity of the associated graded module of a one-dimensional module is given, along with characterizations for when equality is attained. I will outline proofs of these bounds, and the extremal cases. Updated on Nov 09, 2012 02:04 AM PST 317. # Chip-Firing and Binomial Ideals Location: MSRI: Simons Auditorium Speakers: Spencer Backman Chip-firing on graphs has been studied for nearly 25 years since its independent introductions in statistical physics and graph theory. Recently, it has received some attention for its connections to the divisor theory of tropical curves and the combinatorics of lattice ideals. I will give a quick survey of these relationships and briefly describe my current research in chip-firing via gluing with emphasis on the binomial ideal case. Updated on Nov 09, 2012 02:02 AM PST 318. # Higher Laminations and the Fock-Goncharov Duality Conjectures Location: MSRI: Simons Auditorium Speakers: Ian Le Updated on Oct 30, 2012 06:40 AM PDT 319. # Hyperdeterminants of polynomials Location: MSRI: Simons Auditorium Speakers: Luke Oeding Hyperdeterminants were brought into a modern light by Gelʹfand, Kapranov, and Zelevinsky in the 1990\'s. Inspired by their work, I will answer the question of what happens when you apply a hyperdeterminant to a polynomial (interpreted as a symmetric tensor). The hyperdeterminant of a polynomial factors into several irreducible factors with multiplicities. I identify these factors along with their degrees and their multiplicities, which both have a nice combinatorial interpretation. The analogous decomposition for the μ-discriminant of polynomial is also found. The methods I use to solve this algebraic problem come from geometry of dual varieties, Segre-Veronese varieties, and Chow varieties; as well as representation theory of products of general linear groups. Updated on Nov 15, 2012 06:31 AM PST 320. # Two short talks on some geometry Location: MSRI: Simons Auditorium Speakers: Greg Muller Come see two talks for the price of one! (Still free) 'Codimension of deep ideals'. The Laurent embeddings of a cluster algebra A are dual to algebraic tori inside the spectrum of A. The complement of these tori is the 'deep part', where much of the algebraic complexity of A is hiding. I will talk about the codimension of this deep ideal, and an application to computing upper cluster algebras. 'Superunital domains' We will consider the subset of the positive part of a cluster algebra, on which every cluster variable is at least 1. We will talk about why this isn't a completely random thing to do, some results in finite type, and some compelling, mysterious computations." Updated on Nov 01, 2012 06:04 AM PDT 321. # Tensor complexes Location: MSRI: Simons Auditorium Speakers: Manoj Kummini We describe a construction of free resolutions from higher tensors. It provides a unifying view on a wide variety of complexes including the Eagon-Northcott, Buchsbaum-Rim and similar complexes, and the Eisenbud--Schreyer pure resolutions. Updated on Sep 16, 2013 10:17 AM PDT 322. # Relations of minors Location: MSRI: Simons Auditorium Speakers: Winfried Bruns (Universität Osnabrück) Updated on Sep 18, 2013 02:22 PM PDT 323. # Commutative Algebra and Algebraic Geometry (Eisenbud Seminar) Location: UC Berkeley Speakers: Jason McCullough Fix a polynomial ring R = K[x_1...x_n] and a homogeneous ideal I in R. Let d denote the maximal degree of generator of I. A result of Galligo, Giusti and Caviglia-Sbarra shows that reg(R/I) is at most doubly exponential in terms of d and n. Examples due to Mayer and Mayr show that any upper bound must be doubly exponential. However, all extremal examples of resolutions that have large regularity seem to have large regularity early in the resolution. So it makes sense that better upper bounds should be possible if one uses more data about the resolution than just d and n. In this talk, I\'ll show how one can prove two such bounds using the numerics of the Boij-Soederberg decomposition of the Betti table of R/I. Updated on Oct 31, 2012 06:23 AM PDT 324. # Integrability of higher pentagram maps Location: MSRI: Simons Auditorium Speakers: Fedor Soloviev We de fine higher pentagram maps on polygons in any dimension, which extend R. Schwartz's de nition of the 2D pentagram map. These maps turn out to be integrable for both closed and twisted polygons. The corresponding continuous limit of the pentagram map in dimension d is shown to be the (2,d+1)-equation of the KdV hierarchy, generalizing the Boussinesq equation in 2D. In the 3D case we describe the corresponding spectral curve, first integrals, Liouville tori, and the motion along them. This is a joint work with Boris Khesin (University of Toronto). Updated on Oct 31, 2012 05:54 AM PDT 325. # The Geometry of Generic Lagrangian Ffibres: An Illustrating Example Location: MSRI: Simons Auditorium Speakers: Michael Semmel The Geometry of Generic Lagrangian Ffibres: An Illustrating Example Abstract: The aim of the talk is to give an introduction to a strategy developed by M. Adler, P. van Moerbeke and P. Vanhaecke to study the geometry of the generic fibre of a Lagrangian fibration induced by an integrable system. Updated on Oct 31, 2012 09:46 AM PDT 326. # The Arithmetical Rank of the Edge Ideals of Whisker Graphs Location: MSRI: Simons Auditorium Speakers: Antonio Macchia The Arithmetical Rank of the Edge Ideals of Whisker Graphs Abstract: A classical problem in Algebraic Geometry consists in finding the minimum number of hypersurfaces that define a certain variety. This problem can be approached from an Algebraic and Combinatorial point of view. Given a commutative ring R with identity and an ideal I of R, the arithmetical rank of I, denoted ara(I), is the minimum number of elements of R such that the ideal generated by those elements has the same radical as I. The ideal I is called set-theoretic complete intersection (STCI) if ara(I)=ht(I). In general if I is STCI, then I is Cohen-Macaulay, but the converse is not true. I will show that the converse holds for the edge ideals of some whisker graphs. Updated on Nov 01, 2012 09:26 AM PDT 327. # From Briancon-Skoda to Scherk-Varchenko: the story of the monodromy theorem Location: MSRI: Simons Auditorium Speakers: Duco van Straten In the talk I will try to explain in non-technical terms a deep and beautiful relation between the theorem of Briancon-Skoda and the monodromy of an isolated hypersurface singularity {f=0} that was discovered by John Scherk about 30 years ago. A proof of this relation involves the theory of mixed Hodge structures on the vanishing cohomology, but can be understood on an intuitive level. Updated on May 01, 2013 04:41 PM PDT 328. # Commutative Algebra and Algebraic Geometry (Eisenbud Seminar) Location: UC Berkeley Speakers: Vu Thanh Commutative Algebra and Algebraic Geometry Tuesdays, 3:45-6pm in Evans 939 Organizer: David Eisenbud http://hosted.msri.org/alg Date: Tuesday, October 30 3:45 Srikanth Iyengar: Torsion in tensor powers of modules The starting point of this talk is the observation that if a finitely generated module M over a noetherian (commutative!) domain R is NOT free, then its d-fold tensor-product has torsion for each d > rank_RM. In fact, when R is a regular local ring, torsion shows up already when d >= dim R; this is one of the central results in Auslander\\'s 1961 paper "Modules over unramified regular local rings". Recently Celikbas, Piepmeyer, R. Wiegand and I extended this result to certain modules over isolated hypersurface singularities; the preprint will be posted on the arXiv soon. My goal is to discuss some ideas that go into its proof. The main new tool is Hochster\\'s theta-function, and is inspired by recent work of Dao. 5:00 Vu Thanh: Linear resolutions of powers of edge ideals of anti-cycles. Let$I$be the edge ideal of an anticycle of length at least$5$. We will show that all powers$I^k$, for$k \ge 2$have linear resolution. Updated on May 24, 2013 11:03 AM PDT 329. # Cones of Hilbert Functions Location: MSRI: Baker Board Room Speakers: Mats Boij (Royal Institute of Technology (KTH)) Before studying cones of Betti tables over other other rings and with multigradings, it is good to get a picture of what the cone of Hilbert functions looks like. In some cases it is possible to give a complete picture of this cone, but in general the cone is much more complicated than in the standard graded case, suggesting that the corresponding cone of Betti table could be hard to describe. Updated on Oct 25, 2012 03:02 AM PDT 330. # Higher analogues of Teichmuller spaces Location: MSRI: Simons Auditorium Speakers: Bruce Fontaine Updated on Oct 18, 2012 09:46 AM PDT 331. # Three facets of the Lefschetz properties Location: MSRI: Simons Auditorium Speakers: Alexandra Seceleanu The Lefschetz properties are desirable properties of graded artinian algebras, which have strong consequences on the structure of their Hilbert functions. Their investigation is similar in flavor to what one does in algebraic geometry when studying the generic hyperplane section of a projective variety. The talk will provide a gentle introduction to this area of research and will illustrate the beautiful connections which occur when the above mentioned properties are translated into the language of combinatorics, algebraic geometry and representation theory. Some of these connections are quite surprising and still not completely understood. Updated on Oct 18, 2012 04:30 AM PDT 332. # The pentagram map Location: MSRI: Simons Auditorium Speakers: Max Glick The pentagram map, introduced by R. Schwartz, is defined by the following construction: given a polygon as input, draw all of its "shortest" diagonals, and output the smaller polygon which they cut out. I will explain how the machinery of cluster algebras can be used to obtain explicit formulas for the iterates of the pentagram map. The formulas are written in terms of certain cross ratios, and involve generating functions associated with a family of posets which arose in the work of N. Elkies, G. Kuperberg, M. Larsen, and J. Propp on alternating sign matrices. Updated on Oct 19, 2012 04:42 AM PDT 333. # The moduli space of points on the projective line and its ring of invariants. Location: MSRI: Simons Auditorium Speakers: Milena Hering The ring of invariants for the action of the automorphism group of the projective line on the n-fold product of the projective line is a classical object of study. The generators of this ring were determined by Kempe in the 19th century. However, the ideal of relations has been only understood recently in work of Howard, Millson, Snowden and Vakil. They prove that for n>6, the ideal of relations is generated by quadratic equations using a degeneration to a toric variety. I will report on joint work with Benjamin Howard where we compute the Hilbert functions of these rings of invariants, and further study the toric varieties arising in this degeneration. As an application we show that the second Veronese subring of the ring of invariants admits a presentation whose ideal admits a quadratic Gröbner basis. Updated on Oct 18, 2012 05:07 AM PDT 334. # Bertini Theorems over a finite field Location: MSRI: Simons Auditorium Speakers: Daniel Erman (University of Michigan) Over a finite field k, choose a random homogeneous polynomial f of degree d in k[x,y,z]. What is the probability that f defines a smooth planar curve? Questions like this are related to Bertini Theorems over a finite field. The first such Bertini Theorem over a finite field was proved by Bjorn Poonen, who showed that the (asymptotic) probability of smoothness may be realized as a product a of local probabilities. Recent work of myself with Melanie Matchett Wood generalizes this result. I will discuss this collection of ideas, focusing primarily on examples. Updated on Sep 06, 2013 09:44 AM PDT 335. # Commutative Algebra and Algebraic Geometry (Eisenbud Seminar) Location: UC Berkeley Speakers: Sam Payne Commutative Algebra and Algebraic Geometry Tuesdays, 3:45-6pm in Evans 939 Organizer: David Eisenbud http://hosted.msri.org/alg Date: October 23 3:45 Sam Payne: Tropicalization of the moduli space of curves Tropical geometry allows a systematic study of algebraic curves over valued fields in terms of the marked dual graphs of special fibers of models of the curve over the valuation ring. In the past several years, a number of researchers, including Caporaso, Gathmann, Kozlov, Mikhalkin, and their collaborators, have introduced and studied moduli spaces for these marked graphs, which are often called tropical curves, and estabilshed various analogies to moduli spaces of curves. I will present work that explains and extends these analogies, canonically and functorially, by applying a new generalized tropicalization map to the Deligne-Mumford compactification of the moduli space of stable curves. Berkovich spaces appear in the construction of this new tropicalization map in a natural and elementary way, but no tropical or nonarchimedean analytic background is assumed. This is joint work with D. Abramovich and L. Caporaso.} 5:00 Bernd Sturmfels: A Hilbert Scheme in Computer Vision Multiview geometry is the study of two-dimensional images of three-dimensional scenes, a foundational subject in computer vision. We determine a universal Groebner basis for the multiview ideal of n generic cameras. As the cameras move, the multiview varieties vary in a family of dimension 11n-15. This family is the distinguished component of a multigraded Hilbert scheme with a unique Borel-fixed point. We present a combinatorial study of ideals lying on that Hilbert scheme. This is joint work with Chris Aholt and Rekha Thomas. Updated on Sep 11, 2013 10:37 AM PDT 336. # The geometry of cluster algebras and locally acyclic cluster algebras Location: MSRI: Simons Auditorium Speakers: Greg Muller I will begin with cluster localizations', localizations of cluster algebras which are still cluster algebras. Geometrically, a cluster localization of A is dual to an open subscheme of Spec(A) with a cluster structure. Many properties of a cluster algebra can be studied locally with respect to these open patches. This local approach is very effective for locally acyclic cluster algebras'. In this talk, I will define this class, review some of their important properties, give several examples, and present an algorithm for demonstrating that a given cluster algebra is locally acyclic. Updated on Oct 17, 2012 04:42 AM PDT 337. # Recurrence relations and cluster algebras Location: UC Berkeley, 60 Evans Hall Speakers: Pierre Guy Plamondon Sergey Fomin and Andrei Zelevinsky defined cluster algebras by recursively constructing their generators via a process called mutation. This process is closely related to various sequences of integers, arising for instance from Coxeter-Conway friezes, whose terms can be seen as specializations of the generators of specific cluster algebras. Although the fact that these sequences contain only integers is sometimes surprising from their definition, the theory of cluster algebras provides a common explanation for it: the Laurent Phenomenon. In this talk, we will first list some examples of recurrence relations of integers, then we will try to understand them from the point of view of cluster algebras. Updated on Oct 11, 2012 07:05 AM PDT 338. # Combinatorics of the abelian-nonabelian correspondence Location: UC Berkeley Speakers: Kaisa Taipale The UC Berkeley Combinatorics Seminar Mondays 2:10pm - 3:00pm 939 Evans Hall Organizers: Florian Block, Max Glick, and Lauren Williams Combinatorics of the abelian-nonabelian correspondence Speaker: Kaisa Taipale The Grassmannian Gr(k,n) and the product of projective spaces (P^(n-1))^k are both GIT quotients of the projective space P^(nk-1). One can relate their cohomologies and Gromov-Witten theories by the abelian-nonabelian correspondence. I will explain this geometric relationship and two combinatorial manifestations of the correspondence (through Schubert calculus and through torus localization), finishing with some unanswered questions. Updated on Oct 18, 2012 09:22 AM PDT 339. # Equivariant aspects of Boij-Soederberg theory Location: MSRI: Simons Auditorium Speakers: Steven Sam (University of California, Berkeley) I will review the Eisenbud-Floystad-Weyman construction of equivariant pure free resolutions and explain a conjectural generalization to quadric hypersurface rings. I will discuss some current work with Andrew Snowden that tries to realize this generalization. Updated on May 23, 2013 12:44 PM PDT 340. # Quantum dilogarithms and a$q$-deformation of the X-space Location: MSRI: Baker Board Room Speakers: Dylan Rupel Updated on Oct 12, 2012 02:44 AM PDT 341. # Lower Bounds for the Arithmetical Rank of a Homogeneous Ideal in a Polynomial Ring Location: MSRI: Simons Auditorium Speakers: Matteo Varbaro Let I = (f_1,...,f_r) be a homogeneous ideal in the polynomial ring S = K[x_1,...,x_n]. The arithmetical rank of I, ara(I), is the smallest number s such that I has the same radical of the ideal J = (g_1,...,g_s) for some homogeneous polynomials g_1,...,g_s in S. One way to get lower bounds for this number is to look at the non-vanishing of local cohomology with support in I: ara(I) >= t provided that H_I^t(S) is not zero. A similar lower bound comes considering étale topology instead of Zariski's one, and basically these have been, so far, the only two successful methods to compute the arithmetical rank of certain families of ideals. Moreover, in many instances, étale topology was successful where Zariski's one failed. This fact led Lyubeznik to conjecture, in 2002, that the lower bound obtained using étale cohomology is never worse than the one obtained using Zariski's. In the talk I am going to prove that the conjecture is true if the variety defined by I is smooth and K has characteristic 0. Updated on Oct 12, 2012 02:40 AM PDT 342. # The Cyclic Sieving Phenomenon Location: MSRI: Simons Auditorium Speakers: Bruce Fontaine In 2004, Reiner, Stanton and White noticed that to an action of a cyclic group on a finite set one can often attach a polynomial with nonnegative integer coefficients. This polynomial has the property that when it is evaluated at specific roots of unity, the result is the size of the fixed point set for an element of the group. I will introduce the notion of 'promotion' on Young tableaux and via representation theory and geometry show that the polynomial attached to this action is the Kostka-Foulkes polynomial. This is joint work with Joel Kamnitzer Updated on Oct 12, 2012 02:42 AM PDT 343. # Duality in Boij--Soederberg Theory (detailed) Location: MSRI: Simons Auditorium Speakers: Daniel Erman (University of Michigan) This will be a more technical version of my talk from Monday. I will begin by giving detailed descriptions of the duality pairing and some of the repercussions for studying cones of Betti tables. The rest of the talk will be more casual in nature (like a working seminar) and will depend on the questions and interests of the audience. Updated on Sep 06, 2013 09:44 AM PDT 344. # Bounds on the number of generators of ideals Location: MSRI: Simons Auditorium Speakers: Giulio Caviglia We will present several methods to obtain uniform (sharp) upper bounds for the number of generators of ideals. These bounds will depend on fixing some invariants of the ideal, for instance the Hilbert function or the Hilbert polynomial, both in the graded and in the local setting. In particular we will show how classical results such as Macaulay's Theorem and some of its recent generalizations follow from a unified approach. Updated on Oct 11, 2012 02:40 AM PDT 345. # Commutative Algebra and Algebraic Geometry (Eisenbud Seminar) Location: UC Berkeley Speakers: Jose Rodriguez Commutative Algebra and Algebraic Geometry Tuesdays, 3:45-6pm in Evans 939 Organizer: David Eisenbud http://hosted.msri.org/alg Date: Oct 16 3:45: Anurag Singh: The F-pure threshold of a Calabi-Yau hypersurface The F-pure threshold is a numerical invariant of prime characteristic singularities. It constitutes an analogue of a numerical invariant for complex singularities---the log canonical threshold---that measures local integrability. We will discuss, in detail, the calculation of F-pure thresholds of elliptic curves, and also indicate how this calculation extends to Calabi-Yau hypersurfaces. This is work in progress with Bhargav Bhatt. 5:00 Jose Rodriguez: Maximum Likelihood for Matrices with Rank Constraints Maximum likelihood estimation is a fundamental computational task in statistics and it also involves some beautiful mathematics. We discuss this task for determinantal varieties (matrices with rank constraints) and show how numerical algebraic geometry can be used to maximize the likelihood function. Our computational results with the software Bertini led to surprising duality conjectures. This is joint work with Bernd Sturmfels and Jon Hauenstein. Updated on May 23, 2013 01:31 PM PDT 346. # Brane Tilings and Cluster Algebras Location: MSRI: Simons Auditorium Speakers: Gregg Musiker (University of Minnesota Twin Cities) We present work in progress on combinatorial formulas for cluster variables arising from certain periodic cluster algebras. These formulas are phrased in terms of brane tilings which arise in the string theory literature. No prior knowledge of brane tilings or string theory will be assumed, and some connections to cluster algebras and quivers will be explained. Part of this talk is based on work with In-Jee Jeong and Sicong Zhang from the 2011 and 2012 REU's at University of Minnesota. Updated on Sep 10, 2013 01:57 PM PDT 347. # Categorification of quiver mutation Location: UC Berkeley, 60 Evans Hall Speakers: Idun Reitin The cluster algebras were introduced by Fomin-Zelevinsky in a paper which appeared 10 years ago. There are connections to many different areas of mathematics, including quiver representations. One direction of research has been to try to model the ingredients in the definition of cluster algebras in “nice” categories, like module categories or related categories. In this lecture we illustrate the idea and use of “categorification” by concentrating on only one ingredient in the definition of cluster algebras. This is the operation of quiver mutation, which we define. For finite quivers (i.e. directed graphs) without oriented cycles this leads to the so-called cluster categories, which are modifications of certain module categories. For other types of quivers some stable categories of maximal Cohen-Macaulay modules over commutative Gorenstein rings are the relevant categories. We start the lecture with background material on quiver representations. Updated on Oct 05, 2012 01:41 AM PDT 348. # Inverse problem in cylindrical electrical networks Location: UC Berkeley Speakers: Pavlo Pylyavskyy The UC Berkeley Combinatorics Seminar Mondays 2:10pm - 3:00pm 939 Evans Hall Organizers: Florian Block, Max Glick, and Lauren Williams Inverse problem in cylindrical electrical networks Speaker: Pavlo Pylyavskyy The inverse Dirichlet-to-Neumann problem in electrical networks asks one to recover the combinatorial structure of a network and its edge conductances from its response matrix. For planar networks embedded in a disk, the problem was studied and effectively solved by Curtis-Ingerman-Morrow, de Verdière-Gitler-Vertigan and Kenyon-Wilson. I will describe how the problem can be solved for a large class of networks embedded in a cylinder. Our approach uses an analog of the R-matrix for certain affine geometric crystals. It also makes use of Kenyon-Wilson\\'s groves. This is joint work with Thomas Lam. Updated on Sep 21, 2012 04:01 AM PDT 349. # Duality in Boij--Soederberg Theory (overview) Location: MSRI: Simons Auditorium Speakers: Daniel Erman (University of Michigan) A central idea in Boij-Soederberg Theory is that there is a connection between free resolutions over the polynomial ring and sheaf cohomology on projective space. This idea emerged from Eisenbud and Schreyer's proof of the Boij-Soederberg conjectures. In joint work with David Eisenbud, we give a new perspective on this duality. I will outline the resulting duality between syzygies and sheaf cohomology, and I will explain how our duality pairing enables us to extend the scope of Boij--Soederberg theory in several directions. Updated on Sep 06, 2013 09:44 AM PDT 350. # Dilogarithms Location: MSRI: Baker Board Room Speakers: Florian Block Updated on Oct 05, 2012 05:36 AM PDT 351. # Minimal elements of linkage classes. Location: MSRI: Simons Auditorium Speakers: Paolo Mantero (University of California) Linkage is a theory at the borders between Algebraic Geometry and Commutative Algebra aiming at classifying ideals (varieties) and their properties, based on an operation of "linkage". Since ideals in the same linkage class share several homological properties, it is important to identify the minimal elements in a linkage class (that is, the best' and simplest' elements in it). For example, ideals in the linkage class of a complete intersection (=licci ideals) can be very complicated, however, because of linkage they share several interesting (and subtle) properties of complete intersection ideals. Extensive work by several authors (Ballico, Bolondi, Hartshorne, Lazarsfeld, Martin-Deschamps, Migliore, Nagel, Perrin, Rao, Strano, etc.) provides a well-understood notion of minimality in the case of (homogeneous) ideals of codimension 2, However, in the general case (=non-licci ideals of codimension > 2) it is not even clear what could be a good definition of minimality and, consequently, if minimal elements exist in any linkage class. Polini and Ulrich found special ideals that are "minimal" in several regards. However, the question of finding a general notion of minimality was wide-open. In the present talk, we suggest a general notion of minimality for Cohen-Macaulay ideals, which includes the classes of ideals found by Polini-Ulrich . We prove, under reasonable assumptions, that minimal elements exist and are essentially unique. We then provide several concrete classes of ideals which are minimal. We will show applications to the question of when two ideals lie in the same even linkage class, and the Buchsbaum-Eisenbud-Horrocks' Conjecture (which suggests lower bounds for the Betti numbers of any Cohen-Macaulay ideal). Updated on Oct 05, 2012 02:02 AM PDT 352. # Categorification to Rank 2 Quantum Cluster Algebras Location: MSRI: Simons Auditorium Speakers: Dylan Rupel The categorification of cluster algebras provides a powerful tool for understanding the subtle relationships between the elements of the cluster algebra. In the case of quantum cluster algebras, the categorification is only known for acyclic types. In this talk we will restrict to the special case of rank two quantum cluster algebras (with two variables in each cluster and no coefficients). I will develop the theory of quantum cluster algebras "from scratch", in particular giving a short elementary proof of the Laurent phenomenon. I will introduce the notion of valued quivers and the basic features of their representation theory, namely reflection functors. I will show how one can construct non-initial cluster variables from the representations of a valued quiver, and if there is time, I will indicate how to prove this result using only the reflection functors. Updated on Oct 05, 2012 07:13 AM PDT 353. # On the arithmetic of hyperelliptic curves: Arithmetic invariant theory (Bowen Lecture) Location: UC Berkeley Speakers: Benedict Gross Series Title: On the arithmetic of hyperelliptic curves Thursday October 11th Lecture 3: Arithmetic invariant theory 60 Evans Hall Abstract: I will describe a representation of the orthogonal group whose stable orbits are related to the 2-descent on hyperelliptic curves of a fixed genus with a rational Weierstrass point, and construct the principal homogeneous spaces for the Jacobian using pencils of quadrics. Updated on Oct 03, 2012 04:10 AM PDT 354. # Superflatness Location: MSRI: Simons Auditorium Speakers: Adam Boocher Passing from an ideal I to an initial ideal can be thought of as a flat degeneration, and as such it preserves the Hilbert function. In this talk we'll take a peek at what happens when other invariants are also preserved. Using determinantal ideals as our guide, I'll present lots of examples, and close with some new results on toric ideals. Updated on Oct 03, 2012 02:18 AM PDT 355. # On the arithmetic of hyperelliptic curves: Hyperelliptic curves with a rational Weierstrass point (Bowen Lecture) Location: UC Berkeley Speakers: Benedict Gross Series Title: On the arithmetic of hyperelliptic curves Wednesday October 10th Lecture 2: Hyperelliptic curves with a rational Weierstrass point 105 North Gate Hall Abstract: I will review the equations that define these curves, and describe the subgroup of 2-torsion in their Jacobians. After a review of the 2-descent, I will state the results which Bhargava and I have obtained on the average value of the order of the 2-Selmer group, and give some corollaries on the rational points of the curve and its Jacobian. Updated on Oct 03, 2012 04:08 AM PDT 356. # Cones of Betti numbers and Hilbert functions Location: MSRI: Simons Auditorium Speakers: Mats Boij (Royal Institute of Technology (KTH)) The Hilbert function and the graded Betti numbers are invariants we use to study graded rings and modules. When we look at graded modules generated in degree zero over the standard graded polynomial ring, we know by Macaulay's classification exactly what the possible Hilbert functions are. However, for the graded Betti numbers, we are far from having such a complete description. What we do have, is a clear picture of what the set of Betti tables looks like up to scaling, i.e., the cone spanned by all Betti tables in a suitable vector space over the rational numbers. I will explain this picture and give an overview of the sequence of steps that led to it. When changing the grading, we don't even know much about the possible Hilbert functions and it therefore interesting to study also Hilbert functions up to scaling. Updated on Oct 03, 2012 02:15 AM PDT 357. # On the arithmetic of hyperelliptic curves: The rank of elliptic curves (Bowen Lecture) Location: UC Berkeley Speakers: Benedict Gross Series Title: On the arithmetic of hyperelliptic curves Tuesday October 9th Lecture 1: The rank of elliptic curves 50 Birge Hall Abstract: I will review why elliptic curves are somewhat special, define the rank of a curve over the rational numbers, and motivate the conjecture of Birch and Swinnerton-Dyer on the L-function. After stating what is known, I will briefly introduce a new method, due to Manjul Bhargava, for studying the average rank. Updated on Oct 03, 2012 04:06 AM PDT 358. # Commutative Algebra and Algebraic Geometry (Eisenbud Seminar) Location: UC Berkeley Speakers: Giulio Caviglia, Bernd Sturmfels (UC Berkeley Math Faculty) October 9 3:45: Bernd Sturmfels A Hilbert Scheme in Computer Vision Multiview geometry is the study of two-dimensional images of three-dimensional scenes, a foundational subject in computer vision. We determine a universal Groebner basis for the multiview ideal of n generic cameras. As the cameras move, the multiview varieties vary in a family of dimension 11n-15. This family is the distinguished component of a multigraded Hilbert scheme with a unique Borel-fixed point. We present a combinatorial study of ideals lying on that Hilbert scheme. This is joint work with Chris Aholt and Rekha Thomas. 5pm: Giulio Caviglia Koszul property of projections of the Veronese cubic surface Let V be the Veronese cubic surface in P^9. We classify the projections of V to P^8 whose coordinate rings are Koszul. In particular we obtain a purely theoretical proof of the Koszulness of the pinched Veronese, a result obtained originally by using filtrations, deformations and computer assisted computations. To this purpose we extend, to certain complete intersections, results of Conca, Herzog, Trung and Valla concerning homological properties of diagonal algebras. This is a joint work with Aldo Conca. Updated on Sep 11, 2013 10:37 AM PDT 359. # Cluster structures in rings of SL_3 invariants Location: MSRI: Simons Auditorium Speakers: Sergey Fomin (University of Michigan) The rings of polynomial SL(V)-invariants of configurations of vectors and linear forms in a k-dimensional complex vector space V have been explicitly described by Hermann Weyl in the 1930s. Each such ring conjecturally carries a natural cluster algebra structure (typically, many of them) whose cluster variables include Weyl's generators. In joint work with Pavlo Pylyavskyy, we describe and explore these cluster structures in the case k=3. We employ the machinery of tensor diagrams, and make a connection to the web bases introduced by G. Kuperberg. Updated on Nov 09, 2013 10:51 AM PST 360. # On singularity confinement for the pentagram map Location: UC Berkeley Speakers: Max Glick The UC Berkeley Combinatorics Seminar Mondays 2:10pm - 3:00pm 939 Evans Hall Organizers: Florian Block, Max Glick, and Lauren Williams On singularity confinement for the pentagram map Speaker: Max Glick The pentagram map, introduced by R. Schwartz, is a birational map on the configuration space of polygons in the projective plane. We study the singularities of the iterates of the pentagram map. We show that a typical singularity disappears after a finite number of iterations, a confinement phenomenon first discovered by Schwartz. We provide a method to bypass such a singular patch by directly constructing the first subsequent iterate that is well defined on the singular locus under consideration. The key ingredient of this construction is the notion of a decorated (twisted) polygon, and the extension of the pentagram map to the corresponding decorated configuration space. Updated on Sep 28, 2012 03:41 AM PDT 361. # Laminations and the Fock-Goncharov Conjectures for Surfaces and SL_2 Location: MSRI: Simons Auditorium Speakers: Gregg Musiker (University of Minnesota Twin Cities) Updated on Sep 10, 2013 01:57 PM PDT 362. # The poset of Hilbert functions in graded algebras. Location: MSRI: Simons Auditorium Speakers: Manoj Kummini For a standard graded algebra R, we consider embeddings of the the poset of Hilbert functions of quotients of R into the poset of ideals of R, as a way of studying Hilbert functions. We will look at what happens when we take ring extensions. This is joint work with G. Caviglia. Updated on Sep 27, 2012 08:06 AM PDT 363. # A Gentle Introduction to Quantum Cohomology Location: MSRI: Simons Auditorium Speakers: Kaisa Taipale This talk will be an introductory discussion of quantum cohomology and Gromov-Witten invariants with a focus on homogeneous varieties. These ideas have enumerative interpretations and rich combinatorial structure. No new results will be discussed; the aim instead is an exposition of a beautiful area of mathematics that informs mirror symmetry and has yet-to-be-discovered connections with cluster algebras. Updated on Sep 26, 2012 06:37 AM PDT 364. # Integral closures of ideals and modules Location: MSRI: Simons Auditorium Speakers: Bernd Ulrich (Purdue University) We will discuss seemingly unrelated contexts in which integral closures of ideals and modules arise naturally. We will emphasize on the connection with differentials and multiplicities, and address computational issues if time permits. Updated on May 28, 2013 10:20 AM PDT 365. # Continuous Cluster Categories Location: MSRI: Simons Auditorium Speakers: Gordana Todorov (Northeastern University) Updated on Apr 30, 2013 04:44 PM PDT 366. # Introduction to cluster algebras Location: UC Berkeley, 60 Evans Hall Speakers: Andrei Zelevinsky Cluster algebras are a class of commutative rings discovered by Sergey Fomin and the speaker about a decade ago. A cluster algebra of rank n has a distinguished set of generators (cluster variables) grouped into (possibly overlapping) n-subsets called clusters. These generators and relations among them are constructed recursively and can be viewed as discrete dynamical systems on a n-regular tree. The interest to cluster algebras is caused by their surprising appearance in a variety of settings, including quiver representations, Poisson geometry, Teichmuller theory, non-commutative geometry, integrable systems, quantum field theory, etc. We will discuss the foundations of the theory of cluster algebras, with the focus on their algebraic and combinatorial structural properties. Updated on Sep 11, 2013 09:10 AM PDT 367. # Tropicalization method in cluster algebras Location: UC Berkeley Speakers: Tomoki Nakanishi The UC Berkeley Combinatorics Seminar Mondays 2:10pm - 3:00pm 939 Evans Hall Organizers: Florian Block, Max Glick, and Lauren Williams Tropicalization method in cluster algebras Speaker: Tomoki Nakanishi In cluster algebras, after making several mutations of sends, you may sometimes end up with the initial seed. That is the periodicity phenomenon in cluster algebras. Periodicity is a rare event, but once you have it, you can also get the associated dilogarithm identity, plus its quantum version, for free! There are two basic questions for periodicity: How to find it and how to prove it? The answer to the second question is given by the tropicalization method, which I explain in this talk by several examples. The first question is more difficult, and I do not know the answer. However, we are lucky to have several (infinitely many) conjectured periodicities from the Bethe ansatz method in 90\'s, even before the birth of cluster algebras, and they are recently proved by the tropicalization method. There is always some root system behind the scene. The talk is based on the work with R. Inoue, O. Iyama, B. Keller, and A. Kuniba. Updated on Sep 21, 2012 03:54 AM PDT 368. # Linkage of ideals. Location: MSRI: Simons Auditorium Speakers: Paolo Mantero (University of California) Linkage (or liaison) is an elegant theory standing on the border between Commutative Algebra and Algebraic Geometry. Its roots go back to the nineteenth century, although the first modern treatment appeared in 1974, in a celebrated paper written by Peskine and Szpiro. Since then, linkage has been an active area of research and has proved to be a powerful tool, successfully employed in a number of circumstances, ranging from structure theorems, to results on Hilbert scheme (smoothness, irreducible components, etc.). Moreover, in the last 20 years, the original theory developed two interesting, very different, generalizations, namely, linkage by Gorenstein ideals (or G-liaison) and residual intersection theory. Starting from the definition of linkage, we will introduce the theory, provide examples, discuss several results, and explain some of the main open questions in the theories of liaison and G-liaison. Updated on Sep 25, 2012 03:09 AM PDT 369. # The Fock-Goncharov Conjectures in type A_n Location: MSRI: Baker Board Room Speakers: Hugh Thomas Updated on Sep 21, 2012 08:39 AM PDT 370. # Canonical bases of cluster algebras via tropical geometry. Location: MSRI: Simons Auditorium Speakers: Mark Gross I will talk about ongoing work with Hacking, Keel and Kontsevich on an approach to constructing canonical bases of cluster algebras using ideas which originate in mirror symmetry. We use the technology of "scattering diagrams" and "broken lines". Scattering diagrams arose in work of Kontsevich and Soibelman to construct mirror pairs of K3 surfaces, but are now being applied much widely. In particular, seed datum for a cluster algebra generates a particularly nice scattering diagram, which incorporates but has more information than the cluster complex. Broken lines are then tropical objects in the scattering diagram whose enumeration can be used to produce canonical bases. Updated on Sep 21, 2012 02:12 AM PDT 371. # (Multigraded) Hilbert functions Location: UC Berkeley, 60 Evans Hall Speakers: Diane Maclagan Commutative algebra often abstracts geometric problems into simple questions about algebraic invariants. I will illustrate this with some open problems on the Hilbert function (a simple algebraic invariant which measures the dimensions of graded pieces of a graded ring). Geometry enters the picture when the ring is the projective coordinate ring of a variety. When the ring has a multigrading we also get some interesting combinatorics. I will emphasize the computational and combinatorial sides of this story. Updated on Sep 10, 2013 10:21 AM PDT 372. # Syzygies, singularities and implicitization for tensor product surfaces Location: MSRI: Simons Auditorium Speakers: Alexandra Seceleanu A central problem in geometric modeling is to find the implicit equations for a curve or surface defined parametrically. From the standpoint of commutative algebra, there is a strong connection between the implicit equation and the syzygies of the base locus of the parametrization. This relation is made explicit by the theory of approximation complexes, as developed by Herzog-Simis-Vasconcelos, Buse-Jouanolou, Cox, Chardin. I will give an overview of the use of syzygies in implicitization and illustrate with the case of tensor product surfaces. For tensor product surfaces of small degree, we can determine explicitly all bigraded minimal free resolutions of the base ideal. We study the singularities of these surfaces in relation to the syzygies and obtain a simplified implicit equation. The work on tensor product surfaces is joint with H. Schenck and J. Validashti. Updated on Sep 20, 2012 02:52 AM PDT 373. # Bounds on the Projective Dimension of Ideals Location: MSRI: Simons Auditorium Speakers: Jason McCullough Given a homogeneous ideal I in a polynomial ring R over a field, one can compute a minimal graded free resolution of I (or R/I). The length of this resolution, called the projective dimension, is finite and at most the number of variables of R by Hilbert's Syzygy Theorem. When I has few generators in low degree, one expects that projdim(R/I) cannot be arbitrarily large, even when R has many variables. Stillman asked precisely for a bound on projdim(R/I) in terms of the degrees of the minimal generators of I. In this talk I will survey the history of this problem and recent developments toward a solution, including the exponential bound of Ananyan-Hochster in the case of ideals generated by quadrics, specific bounds for three-generated ideals in low degree by Eisenbud-Huneke and Engheta, and families of ideals with large projective dimension. Updated on Sep 14, 2012 06:56 AM PDT 374. # Parametrization of generic bases for cluster algebras Location: MSRI: Simons Auditorium Speakers: Pierre-Guy Plamondon Updated on Sep 20, 2012 02:43 AM PDT 375. # Commutative Algebra Open Problems Session Location: MSRI: Simons Auditorium Speakers: Craig Huneke (University of Virginia) Updated on Nov 21, 2013 09:29 AM PST 376. # Tropical Geometry Seminar Location: MSRI: Baker Board Room Tropical Seminar schedule Location: Baker board room 10:00 Diane Maclagan (Warwick) "Commutative algebra aspects of tropical geometry" 10:45 Qingchun Ren (UC Berkeley) "The intrinsic torus of a very affine variety" 11:15 Florian Block (UC Berkeley) "The Euler characteristic of a very affine variety" 12:00 Rei Inoue (Chiba) "Tropical Geometry and Integrable systems" 12:45 - Tropical discussion over lunch (bring or order your own) Updated on Sep 13, 2012 09:25 AM PDT 377. # Positivity and greedy bases in rank 2 cluster algebras Location: MSRI: Simons Auditorium Speakers: Andrei Zelevinsky The original motivation for the study of cluster algebras was to design an algebraic framework for understanding total positivity and canonical bases. A lot of recent activity in the field has been directed towards various constructions of natural" bases in cluster algebras. One of the approaches to this problem was developed several years ago in a joint work with P.Sherman where it was shown that the indecomposable positive elements form a basis over integers in any rank 2 cluster algebra of finite or affine type. It is strongly suspected (but not proved) that this property does not extend beyond affine types. In a joint work with K.Lee and L.Li we go around this difficulty by constructing a new basis in any rank 2 cluster algebra, which we call the greedy basis. It consists of a special family of indecomposable positive elements that we call greedy elements. Inspired by a recent work of K.Lee - R.Schiffler and D.Rupel, we give an explicit combinatorial expression for greedy elements using the language of Dyck paths. Updated on Sep 11, 2013 09:10 AM PDT 378. # Mustafin Varieties Location: MSRI: Simons Auditorium Speakers: Bernd Sturmfels (UC Berkeley Math Faculty) A Mustafin variety is a degeneration of projective space induced by a point configuration in a Bruhat-Tits building. The special fiber is reduced and Cohen-Macaulay, and its components form beautiful combinatorial patterns. For configurations in one apartment, these patterns are mixed subdivisions of simplices, and there is a tight connection to tropical convexity. In general, the components of the special fiber are rational varieties, and any blow-up of projective space along a linear subspace arrangement can arise. We present a study of the two-dimensional building for PGL(3), joint with Dustin Cartwright, Mathias Haebich and Annette Werner, that classifies Mustafin triangles into 38 combinatorial types. Updated on Sep 11, 2013 10:37 AM PDT 379. # Commutative Algebra and Algebraic Geometry (Eisenbud Seminar) Location: UC Berkeley Speakers: Elizabeth Gross Commutative Algebra and Algebraic Geometry Tuesdays, 3:45-6pm in Evans 939 Organizer: David Eisenbud Sept 18 3:45: Aldo Conca: Syzygies of Koszul algebras Koszul algebras are certain algebras defined by quadratic relations; most quadratic algebras that arise naturally are in fact Koszul. There is no finite criterion for Koszulness, however, so it is interesting to study necessary or sufficiently conditions. I will explain what Koszul algebras are, and describe special features of their syzygies. 5:00: Elizabeth Gross: Toric Ideals of Hypergraphs The edge subring of a graph G is the monomial subalgbera parameterized by the edges of G. It’s defining ideal, commonly referred to as the toric ideal of G, has been well-studied and several historical results tell us the same beautiful story: we can understand these ideals by understanding the combinatorics of the underlying graph. A natural extension is to consider the toric ideal of a hypergraph. In this talk, we will survey well-known results on the toric ideals of graphs and explain how these concepts generalize to hypergraphs. We will end with recent results on the toric ideals of hypergraphs. Updated on Sep 14, 2012 02:26 AM PDT 380. # Ulrich ideals and modules. Location: MSRI: Simons Auditorium Speakers: Shiro Goto (Meiji University) Updated on Sep 12, 2012 09:40 AM PDT 381. # 5-minute talks Location: MSRI: Simons Auditorium Updated on Aug 30, 2012 04:57 AM PDT 382. # 5-minute talks Location: MSRI: Simons Auditorium Updated on Aug 30, 2012 04:56 AM PDT 383. # Laurent phenomenon algebras II Location: MSRI: Simons Auditorium Speakers: Pavlo Pylyavskyy In a joint work with Thomas Lam we use a deformation of Serre relations to define a family of Lie groups acting on planar electrical networks. In this talk I will explain how coordinate rings of those groups can be naturally endowed with Laurent phenomenon algebra structures. A combinatorial model for certain seeds of those algebras in terms of wiring diagrams has been studied by Henriques and Speyer under the name multidimensional cube recurrence. Our machinery of Laurent phenomenon algebras allows to extend this dynamics beyond the part modeled by wiring diagrams. Updated on Sep 04, 2012 06:39 AM PDT 384. # Vanishing of Tor, and why we care about it Location: MSRI: Simons Auditorium Speakers: Roger Wiegand Updated on Sep 05, 2012 06:14 AM PDT 385. # Laurent phenomenon algebras I Location: MSRI: Simons Auditorium Speakers: Pavlo Pylyavskyy In a joint work with Thomas Lam we generalize Fomin and Zelevinsky's cluster algebras by allowing exchange polynomials to be arbitrary irreducible polynomials, rather than binomials. In the first talk I will explain the definition, and then concentrate on Laurent phenomenon algebras with linear seeds. The polytopes dual to cluster complexes of those algebras are essentially the nestohedra previously studied by Feichtner - Sturmfels, Postnikov and Zelevinsky. Updated on Sep 04, 2012 06:38 AM PDT 386. # QUASI PERIODIC ORBITS: THE CASE OF THE NON LINEAR SCHRÖDINGER EQUATION Location: UC Berkeley, 60 Evans Hall Speakers: Claudio Procesi Updated on Aug 24, 2012 05:52 AM PDT 387. # Hilbert coefficients : classical results and open problems Location: MSRI: Simons Auditorium Speakers: Maria Evelina Rossi (Università di Genova) The notion of Hilbert function plays a central role in commutative algebra, in algebraic geometry and in computational algebra. The Hilbert function of a local (or graded) ring is a polynomial function and the coefficients of the corresponding polynomial, called Hilbert coefficients, may capture several numerical and homological invariants of the ring itself. Starting from classical results of S. Abhyankar, D. Northcott and P. Samuel, many papers have been written in this field which is considered an important part of the theory of blowing-up rings. In this talk we present some techniques and we will focus on some open problems which are motivating the recent research on the topic. Updated on Sep 05, 2012 03:38 AM PDT 388. # Open Problems Seminar Updated on Jan 27, 2012 02:40 AM PST 389. # SOME REMARKS ON UNIFORM SPANNING TREES Location: MSRI: Simons Auditorium Speakers: Gregory Lawler (University of Chicago) This will be an informal talk which will not present any new results. I will start by presenting some of the results from Matt Baker\\'s talk on spanning trees and chip-firing games in a more probabilistic way. This part will be self-contained so it is not necessary to have gone to his talk. Assuming sufficient time I will also show how one can deduce the matrix-tree theorem using Wilson\\'s algorithm and relate these to the random walk loop measure whose scaling limit is the Brownian loop measure. (A reference for this is Chapter 9 of my recent book with Vlada Limic.) Updated on Sep 10, 2013 08:43 AM PDT 390. # Multispecies TASEP on a Ring and the Random Shape of an n-core partition Location: MSRI: Simons Auditorium Speakers: Svante Linusson Consider N particles of various classes moving to the left in a ring of length N. A particle of class I can jump over (i.e. trade place with) a particle of class j, if i < j. This is a special case of a so called TASEP (totally assymetric simple exclusion process) and assuming that all the particles jump with the same rate it has a very beautiful solution by Ferrari and Martin in terms of so called multiline queues. The same TASEP comes up as the key to understanding so called reduced random walks in the affine Weyl group of type A in work by Thomas Lam. I will present recent work, in which we have proved a conjecture by Lam about the exact direction for such a walk, by studying this TASEP. As a corollary it also determines the exact shape of a random$n$-core partition. One natural extension is to give the different classes of particles different jump rates. In this situation there exists some very intriguing conjectures by Lam and Williams, which Lauren Williams presented at the MSRI open problem seminar on April 26. I will also describe work where we have found what monomial should be the stationary distribution for which multiline queue, which resolves some (but not all) concjectures by Lam-Williams. This is joint work in different parts with Arvind Ayyer, Omer Angel and James Martin. Updated on May 14, 2012 05:35 AM PDT 391. # Random geometric constructions and analytic capacity: the problems of Painlev\'e, Ahlfors, Denjoy, Vitushkin. Location: MSRI: Simons Auditorium Speakers: Alexander Volberg The talk will be very light because the problems mentioned in the title (ranging over 50 to 110 years old problems) are very hard. Fortunately they are all recently solved. And the key tool is the use of probability methods even though there is absolutely no probability in the setting of the problems. We will see how the key probabilistic idea (a certain random geometric construction) allows us to win over the main difficulties: a total lack of regularity of the setting. Updated on May 09, 2012 02:06 AM PDT 392. # Compatibility of random sequences Location: MSRI: Simons Auditorium Speakers: Vladas Sidoravicius I will present an alternative proof, based on multi-scale analysis, but different from one developed by Basu and Sly, of Winkler\'s compatibility problem. It also applies to Lipschitz embeddings and quasi-isometry problems in 1D. Updated on May 09, 2012 01:56 AM PDT 393. # Lipschitz embeddings of random sequences Location: MSRI: Simons Auditorium Speakers: Allan Sly We develop a new multi-scale framework flexible enough to solve a number of problems involving embedding random sequences into random sequences. As an example we show that there exists an increasing M-Lipschitz embedding from one i.i.d. Bernoulli sequences into an independent copy with positive probability provided that M is large enough. In a closely related problem we show that two independent Poisson processes on R are roughly isometric (or quasi-isometric). Updated on May 10, 2012 06:05 AM PDT 394. # Open Problems Seminar Updated on Jan 27, 2012 02:39 AM PST 395. # Network Discovery in Large and/or Adversarial Real World Networks Location: MSRI: Simons Auditorium Speakers: Alex Waagen A fundamental problem in the study of real-world networks is how to discover topological properties of a network given limited time and resources. For networks which are not too large, a random walker with stationary transition probabilities is usually sufficient. Yet, these methods will not scale up to large graphs, and especially not to modular and directed graphs. I will discuss methods of network discovery in large networks and also in model networks that share features with adversarial networks such as crime or terrorist networks. I will also discuss the use of multiple walkers as a possible analytical tool for studying walks on directed networks. Updated on May 04, 2012 08:44 AM PDT 396. # Regularity of Schramm-Loewner Evolutions and Integration Location: MSRI: Simons Auditorium Speakers: Brent Werness The Schramm-Loewner Evolutions (SLEs) are a one parameter family of random curves which occur as the scaling limits of a number of discrete random processes. While SLE provides excellent information on the geometry of these processes, all information about the original parametrization of the discrete processes is lost. This talk will describe recent work which approaches this issue by answering the question "what is the optimal order of Hölder continuity for SLE curves under an arbitrary reparametrization?" With this result in hand, we will discuss an application to integration along SLE paths and a few related open conjectures. No knowledge of SLE will be assumed. Updated on May 04, 2012 08:35 AM PDT 397. # Stochastically induced bistability in Interacting Population Processes Location: MSRI: Simons Auditorium Speakers: Lea Popovic (Concordia University) We study a stochastic two-species interacting population system, in which species interact within each compartment according to some nonlinear dynamics. In addition we have another mechanism (e.g. migration between compartments) which yield unbiased perturbative changes to species amounts. If each compartment has a large but bounded capacity, then certain combination of these two mechanisms can lead to stochastically induced bistability. In fact, depending on the relative rates between the mechanisms, there are two ways in which bistability can occur, with distinct signatures in terms of spatial correlations. Updated on May 04, 2012 08:29 AM PDT 398. # Edge reinforced random walks, Vertex reinforced jump process, and the SuSy hyperbolic sigma model Location: MSRI: Simons Auditorium Speakers: Pierre Tarres, Toulouse Edge-reinforced random walk (ERRW), introduced by Coppersmith and Diaconis in 1986, is a random process which takes values in the vertex set of a graph G, and is more likely to cross edges it has visited before. We show that it can be represented in terms of a Vertex-reinforced jump process (VRJP) with independent gamma conductances: the VRJP was conceived by Werner and first studied by Davis and Volkov (2002,2004), and is a continuous-time process favoring sites with more local time. Then we prove that the VRJP is a mixture of time-changed Markov jump processes and calculate the mixing measure, which we interpret as a marginal of the supersymmetric hyperbolic sigma model introduced by Disertori, Spencer and Zirnbauer. This enables us to deduce that VRJP and ERRW are strongly recurrent in any dimension for large reinforcement (in fact, on graphs of bounded degree), using a localisation result of Disertori and Spencer (2010). In this talk we will explain in detail the link between ERRW and VRJP, and how the SuSy model arises as limiting measure of VRJP. Joint work with Christophe Sabot Updated on May 04, 2012 08:46 AM PDT 399. # Scale-invariant random spatial networks Location: MSRI: Simons Auditorium Speakers: David Aldous (University of California) Real-world road networks have an approximate scale-invariance property; can one devise mathematical models of random networks whose distributions are exactly invariant under Euclidean scaling? This requires working in the continuum plane. We introduce an axiomatization of a class of processes we call scale-invariant random spatial networks, whose primitives are routes between each pair of points in the plane. We prove that one concrete model, based on minimum-time routes in a binary hierarchy of roads with different speed limits, satisfies the axioms, and note informally that two other constructions (based on Poisson line processes and on dynamic proximity graphs) are expected also to satisfy the axioms. We initiate study of structure theory and summary statistics for general processes in this class. Updated on Sep 04, 2013 09:54 AM PDT 400. # Open Problems Seminar Updated on Jan 27, 2012 02:39 AM PST 401. # Chip-firing games, potential theory on graphs, and spanning trees Location: MSRI: Simons Auditorium Speakers: Matt Baker, UC Berkeley Using the interplay between chip-firing games and potential theory on graphs, we present an "efficient bijective" proof of Kirchhoff\'s matrix-tree theorem and a new algorithm for sampling random spanning trees which does not utilize random walks. This is joint work with Farbod Shokrieh. Updated on Apr 18, 2012 11:58 AM PDT 402. # On a sum of random projections Location: MSRI: Simons Auditorium Speakers: Vladislav Kargin I will talk about fluctuations of eigenvalues of a sum of random matrices. In particular, I will show how the eigenvalues of a sum of random projections are related to the Jacobi random point process, and what are the implications of this relationship for the universality conjecture. Updated on Apr 20, 2012 07:29 AM PDT 403. # Mixing times are hitting times of large setes Location: MSRI: Simons Auditorium Speakers: Perla Sousi We consider irreducible reversible discrete time Markov chains on a finite state space. Mixing times and hitting times are fundamental parameters of the chain. In this talk, we relate them by showing that the mixing time of the lazy chain is equivalent to the maximum over initial states x and large set A of the hitting time of A starting from x. As an application, we show that the mixing time on a finite binary tree is robust to bounded change of edge conductances. (Joint work with Yuval Peres) Updated on Apr 20, 2012 07:29 AM PDT 404. # Ten ways in which the 2d self-avoiding walk should converge to SLE Location: MSRI: Simons Auditorium Speakers: Tom Kennedy The self-avoiding walk is a model of random walks on a lattice in which one only allows walks which do not intersect themselves. It is believed that in two dimensions this model should satisfy a form of conformal invariance, and the scaling limit should be the Schramm-Loewner evolution (SLE) with kappa=8/3. There are a variety of different senses in which the scaling limit should converge to SLE. I will review some of the well known conjectures and present some new conjectures. There are no proofs of any of these conjectures, but most of them are supported by Monte Carlo simulations. Updated on Apr 18, 2012 11:06 AM PDT 405. # Self-Avoiding Walk Location: UC Berkeley, 60 Evans Hall Speakers: Gregory Lawler (University of Chicago) The participants at the Random Spatial Processes program come from many different areas: combinatorics, probability, complex analysis, theoretical physics, computer science, representation theory. Although these give different perspectives, they all arise in the analysis of critical processes in statistical physics. I will discuss a simple (to state, not necessarily to analyze!) model, the self-avoiding walk and show how multiple perspectives are useful in its study. A (planar) self-avoiding walk is a lattice random walk path in the plane with no self-intersections. It can be viewed as a simple model for polymers. I will show how we now in one sense understand this model very well, and in another sense we still know very little! Updated on Sep 10, 2013 08:43 AM PDT 406. # Open Problems Seminar Updated on Jan 27, 2012 02:38 AM PST 407. # Election manipulation: the average-case Location: MSRI: Simons Auditorium Speakers: Miklos Racz The Gibbard-Satterthwaite theorem says that any non-dictatorial way of electing a winner among three or more candidates is subject to manipulation. Recently, there has been much work in finding robust quantitative versions of this theorem, in particular by Friedgut, Kalai, Keller and Nisan for elections with three candidates, and Isaksson, Kindler and Mossel for neutral functions with at least four candidates. I will talk about a quantitative version of the Gibbard-Satterthwaite theorem that holds for any number of (at least three) candidates and does not require the neutrality assumption. The proof combines several ideas from the two previous proofs and also crucially uses reverse hypercontractivity. This is joint work with Elchanan Mossel. Updated on Apr 11, 2012 02:21 AM PDT 408. # Postdoc Seminar Location: MSRI: Simons Auditorium Speakers: Shawn Drenning Updated on Feb 01, 2012 07:47 AM PST 409. # Random lozenge tilings of polygons and their asymptotic behavior Location: MSRI: Simons Auditorium I will discuss the model of uniformly random tilings of polygons drawn on the triangular lattice by lozenges of three types (equivalent formulations: dimer models on the honeycomb lattice, or random 3-dimensional stepped surfaces). Asymptotic questions about these tilings (when the polygon is fixed and the mesh of the lattice goes to zero) have received a significant attention over the past years. We restrict our attention to a certain class of polygons which allows arbitrarily many sides. For a fixed polygon in the class and fixed mesh of the lattice, tilings can be interpreted as interlacing integer arrays {x(j,m) : m=1,...,N, j=1,...,m} (of depth, say, N) with a certain fixed top row. Using a new formula for the determinantal correlation kernel of these uniformly random interlacing integer arrays, we manage to establish the conjectural local asymptotics of random tilings in the bulk (leading to ergodic translation invariant Gibbs measures on tilings of the whole plane), and the predicted behavior of interfaces between so-called liquid and frozen phases (leading to the Airy process). Bulk asymptotic behavior allows to reconstruct the limit shapes of random stepped surfaces obtained by Cohn, Propp, Kenyon, and Okounkov. As a particular case, all our results cover the most investigated case of random boxed plane partitions (when the polygon is a hexagon). Updated on Apr 11, 2012 11:52 AM PDT 410. # Stability of functionals of Markov chains and of stochastic recursions Location: MSRI: Simons Auditorium Speakers: Sergey Foss I will discuss an aprroach the stability study of discrete-time stochastic recursions (including Markov chains) which unifies the now-classical Harris ergodicity and more recent ideas (in contact processes, Markov chains with long memory, infinite bin models, "excited" random walks etc.) which involve conditioning on a finite or infinite past and on a finite or infinite future. Updated on Apr 11, 2012 11:54 AM PDT 411. # Open Problems Seminar Updated on Jan 27, 2012 02:38 AM PST 412. # Robust, dimension-free isoperimetry in Gaussian space Location: MSRI: Simons Auditorium Speakers: Joe Neeman The Euclidean isoperimetric inequality is a famous problem going back more than 2000 years. Its Gaussian analogue, while more recent, has many important applications in probability and computer science. We will discuss the Gaussian isoperimetric problem, including Ledoux's remarkably simple proof, Carlen and Kerce's characterization of the equality case, and a new robustness result which improves, in some sense, work by Cianchi, Fusco, Maggi and Pratelli. Updated on Apr 06, 2012 04:10 AM PDT 413. # Large systems of diffusions interacting through their ranks Location: MSRI: Simons Auditorium Speakers: Mykhaylo Shkolnikov Systems of diffusion processes (particles) with rank-based interactions have been studied heavily due to their importance in stochastic portfolio theory and the intriguing relations with particle systems appearing in statistical physics. We will study the behavior of this particle system as the number of particles gets large. By obtaining a large deviations principle, we will show that the limiting dynamics can be described by a porous medium equation with convection, whereas paths of finite rate are given by solutions of appropriately tilted versions of this equation. This is the first instance of a large deviations principle for diffusions interacting both through the drift and the diffusion coefficients. Based on joint work with A. Dembo, N.V. Krylov, S.R.S. Varadhan and O. Zeitouni. Updated on Apr 06, 2012 06:08 AM PDT 414. # A combinatorial point of view about M. Baker and S. Norine. Riemann Roch Theory for Finite Graphs Location: MSRI: Simons Auditorium Speakers: Robert Cori I will present the results in this paper using simple combinatorial terms. There is a strong connection with the sandpile discrete model largely developped by D. Dhar and the Chip Firing Game on graphs considered by many authors (Biggs Bjorner, Lovasz, Schor) Updated on Apr 03, 2012 09:46 AM PDT 415. # Open Problems Seminar Updated on Jan 27, 2012 02:37 AM PST 416. # Combinatorics of Determinantal facet ideals Location: MSRI: Simons Auditorium Speakers: Fatemeh Mohammadi The Determinantal ideals are generated by a general set of minors of a matrix of indeterminates. In the case that the generators can be identified with the facets of a simplicial complex, it is called a determinantal facet ideal. In this talk I will discuss some algebraic properties of these ideals which can be read directly from their simplicial complexes. One approach is to classify the prime ideals among them. Then I will consider a nice class of simplicial complexes to give a combinatorial description for primary decompositions of their associated ideals. Updated on Mar 30, 2012 01:42 AM PDT 417. # Stochastic Geometric Representations of the Quantum Ising Model in Transverse Field Location: MSRI: Simons Auditorium Speakers: Anna Levit Stochastic geometric methods are known to be a very useful tool for solving a variety of problems in statistical mechanics. Furthermore, problems arising due to this approach are interesting in their own right. First, familiar Fortuin-Kasteleyn (FK) representation for Classical Ising model is presented via the language of Poisson Point Processes. In this way, the usual FK representation emerges as an instance of Lie-Trotter product formula. Next, FK representation is generalized to quantum Ising models in transverse field. This method was originally developed by M. Campanino, A. Klein, J.F. Perez (1991) and M. Aizenman, A. Klein, C.M. Newman (1993). We apply the above Stochastic Geometric reprsentation to the Quantum Curie-Weiss model in transversal field (the Quantum Ising model on complete graph) in order to derive results on the phase diagram of the model. Updated on Mar 30, 2012 01:43 AM PDT 418. # The parafermionic observable in the continuum Location: MSRI: Simons Auditorium Speakers: Brent Werness The parafermionic observable is a tool for explaining the properties of discrete models which are (at least believed to be) conformally invariant in the scaling limit. These models often converge to a form of SLE, and thus it is natural to investigate the degree to which the observable can be seen entirely in the continuum. After providing a definition of the observable for radial SLE, we will show how to derive a closed form formula for the observable even for non-holomorphic choices of the spin. Updated on Mar 28, 2012 04:09 AM PDT 419. # Sampling Paths, Permutations and Lattice Structures Location: UC Berkeley, 60 Evans Hall Speakers: Dana Randall (Georgia Institute of Technology) Random sampling is ubiquitous throughout mathematics, computing and the sciences as a means of studying very large sets. In this talk we will discuss simple, classical Markov chains for efficiently sampling paths and permutations. We will look at various natural generalizations with some surprising results. First, we show how to extend these Markov chain algorithms to sample biased paths, with applications to tile-based self-assembly, asymmetric exclusion processes, self-organized lists, and biased card shuffling. Next, we show how generating random configurations with mutliple paths allows us to sample planar tilings and colorings. Using insights from statistical physics, however, we will see why these methods break down and may be inefficient in models with non-uniform bias, in higher dimensions, or in weighted models with sufficiently high fugacity. Updated on Sep 11, 2013 02:04 PM PDT 420. # The non-existence of symmetric measures on the plane and random geometric constructions Location: UC Berkeley Speakers: Alexander Volberg The measure of dimension s is called s-symmetric if its convolution with s-Riesz kernel is bounded. We show that such measures may exist on the plane only for integer s=1,2. The proof uses systems of random dyadic squares and singular operators with random kernels. This seminar will take place in 740 Evans Hall Updated on Mar 29, 2012 10:01 AM PDT 421. # Chern-Simons Research Lecture Series: Stochastic Schramm-Loewner Evolution (SLE) from Statistical Conformal Field Theory (CFT): An Introduction for (and by) Amateurs. Location: UC Berkeley Speakers: Denis Bernard The lectures will be devoted to a somewhat detailed presentation of Stochastic Schramm-Loewner Evolutions (SLE), which are Markov processes describing fractal curves or interfaces in two-dimensional critical systems. A substantial part of the lectures will cover the connection between statistical mechanics and processes which, in the present context, leads to a connection between SLE and conformal ﬁeld theory (CFT). These lectures aim at ﬁlling part of the gap between the mathematical and physics approaches. They are intended to be at an introductory level. Updated on Mar 15, 2012 09:59 AM PDT 422. # Open Problems Seminar Updated on Jan 27, 2012 02:37 AM PST 423. # Chern-Simons Research Lecture Series: Stochastic Schramm-Loewner Evolution (SLE) from Statistical Conformal Field Theory (CFT): An Introduction for (and by) Amateurs. Location: UC Berkeley Speakers: Denis Bernard The lectures will be devoted to a somewhat detailed presentation of Stochastic Schramm-Loewner Evolutions (SLE), which are Markov processes describing fractal curves or interfaces in two-dimensional critical systems. A substantial part of the lectures will cover the connection between statistical mechanics and processes which, in the present context, leads to a connection between SLE and conformal ﬁeld theory (CFT). These lectures aim at ﬁlling part of the gap between the mathematical and physics approaches. They are intended to be at an introductory level. Updated on Mar 15, 2012 09:58 AM PDT 424. # Dyck tilings, linear extensions, inversions and descents Location: MSRI: Simons Auditorium Speakers: Greta Panova Dyck tilings were introduced by Kenyon and Wilson as a way to count pairing probabilities in the double-dimer model from statistical mechanics. They can be defined purely combinatorially as certain kinds of tilings of skew Young diagrams with ribbon tiles shaped like Dyck paths. We will show two bijections between such Dyck tilings and linear extensions of tree posets. These bijections yield two formulas (conjectured by Kenyon and Wilson) one of which enumerates Dyck tilings with a given lower path by a statistic that translates as descents in linear extensions and the other by a statistic translating into number of inversions. The bijection also leads to generalizations of certain Mahonian statistics to linear extensions. It is also intriguing that certain restrictions of Dyck tilings are in bijection with other objects called Dyck tableaux introduced related to the study of the TASEP model. This is joint work with J.S.Kim,K.Mezsaros,D.B.Wilson. Updated on Mar 14, 2012 07:24 AM PDT 425. # Advanced Matrix Inversion Location: MSRI: Simons Auditorium Speakers: Benjamin Young I will explain how Eric Nordenstam and I guessed and proved a formula for the inverse of a combinatorial matrix with many parameters. We made heavy use of Cramer\'s rule, high-performance computing, the Online Encyclopedia of Integer Sequences, polynomial fitting, and the determinant evaluation techniques of Christian Krattenthaler. Everyone is welcome to attend this talk. Updated on May 29, 2013 09:25 AM PDT 426. # Stability of functionals of Markov chains and of stochastic recursions Location: MSRI: Simons Auditorium Speakers: Sergey Foss I will discuss an aprroach the stability study of discrete-time stochastic recursions (including Markov chains) which unifies the now-classical Harris ergodicity and more recent ideas (in contact processes, Markov chains with long memory, infinite bin models, "excited" random walks etc.) which involve conditioning on a finite or infinite past and on a finite or infinite future. Updated on Mar 16, 2012 03:04 AM PDT 427. # New Extremes for Random Walk on a Graph Location: UC Berkeley, 60 Evans Hall Speakers: Peter Winkler (Dartmouth College) Random walk on a graph is a beautiful and (viewed from today) classical subject with elegant theorems, multiple applications, and a close connection to the theory of electrical networks. The subject seems to be livelier now than ever, with lots of exciting new results. We will discuss recent progress on some extremal problems. In particular, how long can it take to visit every edge of a graph, or to visit every vertex a representative number of times, or to catch a random walker? Can random walks be scheduled or coupled so that they don't collide? Can moving targets be harder to hit than fixed targets? Mentioned will be work by or with Omer Angel, Jian Ding, Agelos Georgakopoulos, Ander Holroyd, Natasha Komarov, James Lee, James Martin, Yuval Peres, Perla Sousi, and David Wilson. Updated on Sep 11, 2013 09:50 AM PDT 428. # Chern-Simons Research Lecture Series: Stochastic Schramm-Loewner Evolution (SLE) from Statistical Conformal Field Theory (CFT): An Introduction for (and by) Amateurs. Location: UC Berkeley Speakers: Denis Bernard The lectures will be devoted to a somewhat detailed presentation of Stochastic Schramm-Loewner Evolutions (SLE), which are Markov processes describing fractal curves or interfaces in two-dimensional critical systems. A substantial part of the lectures will cover the connection between statistical mechanics and processes which, in the present context, leads to a connection between SLE and conformal ﬁeld theory (CFT). These lectures aim at ﬁlling part of the gap between the mathematical and physics approaches. They are intended to be at an introductory level. Updated on Mar 15, 2012 09:57 AM PDT 429. # Open Problems Seminar Updated on Jan 27, 2012 02:36 AM PST 430. # Miscellany on branching random walks Location: MSRI: Baker Board Room Speakers: Ming Fang Branching random walk can be viewed as particles performing random walks while branching at integer time. We review some existing results on the minimal displacement, when each particle moves and branches independently according the same step distribution and the same branching law. Then we will compare them with similar but modified models. In one variation, we will consider the asymptotic behavior of the particle at time n, whose ancestors’ location are consistently small. In another variation, we will consider the maximal displacement for the model, where the step distributions vary macroscopically with respect to time. Updated on Mar 12, 2012 02:26 AM PDT 431. # Weyl metrisability for projective surfaces Location: MSRI: Baker Board Room Speakers: Thomas Mettler For each Riemannian metric g on a manifold there exists a unique torsion-free connection preserving g, the celebrated Levi-Civita connection. Conversely one can try to characterize the connections preserving a metric. A concrete characterization easily applicable to examples was given by L. Eisenhart and O. Veblen in 1922. One can also study the problem of characterizing the connections which are only projectively equivalent to a metric connection (i.e. share the same unparametrized geodesics with a metric connection). The latter problem, albeit first studied by R. Liouville in 1889, was solved only recently by R. Bryant, M. Dunajski and M. Eastwood in the surface case. In this talk, after discussing the aforementioned results, I will show that locally on a surface every connection is projectively equivalent to a connection preserving a conformal structure (a so-called Weyl connection). Surprisingly, the relevant PDE corresponds to the Cauchy-Riemann equations. This allows to classify the Weyl connections on the 2-sphere whose geodesics are the great circles using techniques from algebraic geometry. Updated on Mar 09, 2012 03:33 AM PST 432. # Statistical Mechanics of the Two-Dimensional Coulomb Gas Location: MSRI: Baker Board Room Speakers: Pierluigi Falco The Coulomb gas is the prototype of two-dimensional probabilistic model displaying a special kind of phase transition, the 'Kosterlitz-Thouless' one. In this presentation I will review conjectures, results and works in progress on this model, with emphasis on universality aspects. Updated on Mar 09, 2012 01:37 AM PST 433. # Open Problems Seminar Updated on Jan 27, 2012 02:36 AM PST 434. # Biased domino tilings of the Aztec Diamond Location: MSRI: Simons Auditorium Speakers: Sunil Chhita Domino tilings on the Aztec Diamond have been extensively studied over the past twenty years. Tilings of large Aztec diamonds exhibit four frozen regions and an elliptic liquid region. In this talk, we focus on the interface between the liquid and frozen regions, explaining some of the new behavior we have observed. This is joint work with Benjamin Young and Kurt Johansson. Updated on Mar 01, 2012 04:09 AM PST 435. # Scaling window for mean-field percolation of averages Location: MSRI: Simons Auditorium Speakers: Jian Ding For a complete graph of size$n$, assign each edge an i.i.d. exponential variable with mean$n$. For$\lambda>0$, consider the length of the longest path whose average weight is at most$\lambda$. It was show by Aldous (1998) that the critical value of$\lambda$is$1/e$, below which the length is logarithmic and above which the length is linear. We show that at criticality the order of the length is$(\log n)^3$where the scaling window (for$\lambda$) is of size$(\log n)^{-2}$. Furthermore, we establish a polynomial lower bound on the length when$(\lambda - 1/e) (\log n)^2$exceeds a certain constant, which implies a second phase transition at criticality. Our results answer a question of Aldous (2003). Updated on Mar 01, 2012 03:27 AM PST 436. # Estimating the probability of the needle to land near a Cantor set Location: MSRI: Simons Auditorium Speakers: Alexander Volberg The problem of estimating the average length of the projection of C^n small discs located in the Cantor pattern turns out to mix the combinatorial, complex analytic, and Fourier analytic methods along with some knowledge of diophantine trigonometric equations and a bit of number theory. Still there are many unsolved problems with really simple formulations. I will give an overview of the problems and methods including showing the motivation, which is rooted in some properties of analytic capacity. Updated on Feb 29, 2012 02:47 AM PST 437. # Multi-scale tools and dependent percolation Location: UC Berkeley, 60 Evans Hall Speakers: Maria Vares In this talk I plan to discuss some examples of percolation models in random environment. The goal is to show how multi-scale methods can be used to answer some basic questions related to such models in the presence of strong dependence. Updated on Feb 22, 2012 12:09 PM PST 438. # Noise and Exclusion Sensitivity Location: MSRI: Simons Auditorium Speakers: Jeff Steif (Chalmers University of Technology/University of Göteborg) In the first half of the talk, I will give a very brief overview of noise sensitivity of Boolean functions and relations to percolation. In the second half of the talk, I will describe soon to appear joint work with Erik Broman and Christophe Garban concerning the notion of sensitivity under a different dynamics, namely running the exclusion process for a short amount of time. Updated on Sep 13, 2013 09:10 AM PDT 439. # Open Problems Seminar Updated on Jan 27, 2012 02:35 AM PST 440. # Bowen Lecture: Many Particle Systems and Plasma Physics Location: UC Berkeley Speakers: Cedric Villani Updated on Jan 27, 2012 12:44 AM PST 441. # Postdoc Seminar Location: MSRI: Simons Auditorium Updated on Feb 01, 2012 07:40 AM PST 442. # Postdoc Seminar Location: MSRI: Simons Auditorium Updated on Feb 01, 2012 07:41 AM PST 443. # Bowen Lecture: Many Particle Systems and Plasma Physics Location: UC Berkeley Speakers: Cedric Villani Updated on Jan 27, 2012 12:44 AM PST 444. # Mixing time of the card-cyclic to random shuffle Location: MSRI: Simons Auditorium Speakers: Ben Morris - UC Davis We analyze the following method for shuffling$n$cards. First, remove card 1 (i.e., the card with label 1) and then re-insert it randomly into the deck. Then repeat with cards 2, 3,...,$n$. Call this a round. R. Pinsky showed, somewhat surprisingly, that the mixing time is greater than one round. We show that in fact the mixing time is on the order of$\log n$rounds. Joint work with Weiyang Ning and Yuval Peres. Updated on Feb 23, 2012 06:44 AM PST 445. # Extensions of the Duminil-Copin/Smirnov identity for SAWs Location: MSRI: Simons Auditorium Speakers: Anthony Guttmann (University of Melbourne) A recently proved identity due to Duminil-Copin and Smirnov connects different generating functions for self-avoiding walks on the honeycomb lattice. Their identity holds only at the critical step fugacity$x_c,$and was used by them to prove that$x_c=1/(1+\sqrt{2}).$We extend their identity off-criticality, allowing us to prove certain exponent inequalities, and to prove an identity connecting the critical exponent describing the winding-angle of SAW with the exponents for SAW in a half-plane. Other extensions are also mentioned. Updated on Sep 06, 2013 03:34 PM PDT 446. # Bowen Lecture: Many Particle Systems and Plasma Physics Location: UC Berkeley Speakers: Cedric Villani Updated on Jan 27, 2012 12:44 AM PST 447. # Open Problems Seminar Updated on Jan 27, 2012 02:35 AM PST 448. # Infinitely many non-intersecting random walks Location: MSRI: Simons Auditorium Speakers: Vadim Gorin Given N independent one-dimensional random walks (subject to certain technical conditions) it is not hard to condition them never to collide. The resulting conditional process will be both a Markov chain and a determinantal point process. These chains turn out to be related to random matrices and random tilings. In the talk we are going to discuss what happens in the limit when N tends to infinity. The key idea for the construction of the limit object is to link the above Markov chains for various values of N. As we will see, the limit Markov process is also closely related to TASEP with particle-dependent jump rates. The talk is based on the joint work with Alexei Borodin. Everybody (not only postdocs) are welcome to attend my talk! Updated on Feb 08, 2012 01:42 AM PST 449. # Challenges in first-passage percolation Location: MSRI: Simons Auditorium Speakers: Daniel Ahlberg There are several different models describing random spatial growth, of which first-passage percolation is one of the more well studied. However so, there are many questions that almost 50 years after its introduction remain unanswered. I will in this talk present the model, and a few facts that are known. I will also mention some of my own contributions, and further discuss some of the problems that remain open. Updated on Feb 09, 2012 10:10 AM PST 450. # First passage percolation and escape strategies Location: MSRI: Simons Auditorium Speakers: Maria Vares Updated on Feb 09, 2012 05:43 AM PST 451. # Counting tricks with symmetric functions Location: UC Berkeley, 60 Evans Hall Speakers: Greta Panova Symmetric functions and Young tableaux arose from the representation theory of the symmetric and general linear groups, but found their central place in algebraic combinatorics and also ventured to other fields like algebraic geometry and statistical mechanics. In this talk we will review some of their combinatorial properties and then we will employ their power and various tricks to solve a counting problem: we will find a product formula for the number of standard Young tableaux of unusual, truncated shapes and we will pass through truncated plane partitions. Updated on Feb 06, 2012 03:42 AM PST 452. # SLE and conformal welding Location: MSRI: Baker Board Room Speakers: Steffen Rohde (University of Washington) In my talk, I will attempt to give an overview over the state of the art of the Schramm-Loewner Evolution. An emphasis will be on path properties of SLE traces, and we will touch upon definitions of SLE via conformal welding. We will also discuss open questions and speculations. Updated on Sep 11, 2013 03:36 PM PDT 453. # Open Problems Seminar Updated on Jan 27, 2012 02:34 AM PST 454. # The entropy of Schur-Weyl measures Location: MSRI: Simons Auditorium Speakers: Sevak Mkrtchyan Relative dimensions of the isotypic components of the N-th order tensor representations of the symmetric group on n letters give a Plancherel-type measure, called the Schur-Weyl measure, on the set of Young diagrams with n cells and at most N rows. We obtain logarithmic, order-sharp bounds for the maximal dimensions of the isotypic components of the tensor representations and prove that the typical dimensions, after appropriate normalisation, converge to a constant with respect to the Schur-Weyl measures. Updated on Jan 27, 2012 12:47 AM PST 455. # Scaling limit of arbitrary genus random maps Location: MSRI: Simons Auditorium Speakers: Jeremie Bettinelli A map is a gluing of polygons along their edges forming either the sphere or a torus with an arbitrary number of handles. These objects naturally appear in various domains such as mathematics, computer science and physics, and they have been the subject of many studies. During this talk, we will adopt the point of view of scaling limits, consisting roughly in trying to see what a large random map looks like. More precisely, we will address the problem of the convergence, as the size tends to infinity, of rescaled maps chosen uniformly at random in some privileged classes of maps with fixed size. We will see that a scaling limit exists for some specific classes of maps. This defines random metric spaces with interesting properties. We will in particular focus here on their topology. I will expose in this talk the main results of the field and try to give some of the principal ideas behind the study of these objects. Updated on Jan 25, 2012 08:26 AM PST 456. # Abelian networks Location: MSRI: Simons Auditorium Speakers: Lionel Levine An abelian network is a collection of finite automata that live at the vertices of a graph and communicate via the edges. It produces the same output no matter in what order the automata process their inputs. This talk will touch on three basic themes, using chip-firing and rotor-routing as illustrating examples. 1. Halting problem: how to tell whether an abelian network halts on all inputs. 2. Local-to-global principles: certain features of the automata are inherited by the whole network. 3. Critical group: a finite abelian group that governs the long-term behavior of the network. Updated on Jan 26, 2012 04:20 AM PST 457. # From random interlacements to coordinate percolation Location: UC Berkeley, 60 Evans Hall Speakers: Vladas Sidoravicius During the past few years, several percolation models with long (infinite) range dependencies were introduced. Among them Random Interlacements (introduced by A.-S. Sznitman) and Coordinate Percolation (introduced by P. Winkler). During the talk I will focus on the connectivity properties of these models. The latter model has polynomial decay in sub-critical and super-critical regime in dimension 3. I will explain the nature of this phenomenon and why it is difficult to handle these models technically. In the second half of the talk I will present key ideas of the multi-scale analysis which allows to reach some conclusions. At the end of the talk I will discuss applications and several open problems. Updated on Jan 26, 2012 04:24 AM PST 458. # Open Problems Seminar Updated on Jan 17, 2012 02:18 AM PST 459. # Postdoc 5-Minute Talks Location: MSRI: Simons Auditorium Updated on Jan 24, 2012 04:13 AM PST 460. # Postdoc Seminar Created on Jan 19, 2012 01:28 AM PST 461. # Postdoc Seminar Updated on Jan 19, 2012 01:30 AM PST 462. # Rotor-routing, smoothing kernels, and reduction of variance: breaking the O(1/n) barrier Location: MSRI: Simons Auditorium Speakers: James Propp (University of Massachusetts) If a random variable X is easier to simulate than to analyze, one way to estimate its expected value E(X) is to generate n samples that are distributed according to the law of X and take their average. If the samples are independent, then (assuming X has finite variance) the estimate will have typical error O(1/sqrt(n)). But often one can do better by introducing appropriate forms of negative dependence. In the toy context of simulating Markov chains to estimate their absorption probabilities, I\\'ll describe a scheme that uses maximally anticorrelated identically distributed Bernoulli random variables (aka rotor routers) and has typical error O((log n)/n), and a related scheme with typical error O(1/n). This might seem to be optimal, and indeed one cannot expect the average (X_1+...+X_n)/n to differ from its expected value E(X) by less than O(1/n). However, by using weighted averages that assign X_i less weight when i is near 1 or n and greater weight when i is near n/2, one can get estimators for E(X) with typical error significantly smaller than O(1/n). The methods and ideas are mostly probabilistic and combinatorial. No prior knowledge of rotor-routing or smoothing kernels, and no familiarity with (or fondness for) statistics, will be assumed. Updated on Jan 27, 2012 08:21 AM PST 463. # Combinatorics of Donaldson–Thomas and Pandharipande–Thomas invariants Location: UC Berkeley, 60 Evans Hall Speakers: Benjamin Young I will discuss a combinatorial problem which comes from algebraic geometry. The problem, in general, is to show that two theories for "counting" curves in a complex three-dimensional space X (Pandharipande–Thomas theory and reduced Donaldson–Thomas theory) give the same answer. I will prove a combinatorial version of this correspondence in a special case (X is toric Calabi–Yau), where the difficult geometry reduces to a study of the topological vertex\'\' (a certain generating function) in these two theories. The combinatorial objects in question are plane partitions, perfect matchings on the honeycomb lattice and related structures. There will be many pictures. This is a combinatorics talk, so no algebraic geometry will be used once I explain where the problem is coming from. Updated on May 29, 2013 09:25 AM PDT 464. # Postdoc Seminar Location: MSRI: Simons Auditorium Updated on Aug 31, 2011 10:13 AM PDT 465. # Definitions of Quasiregularity in Metric Spaces Location: MSRI: Simons Auditorium Speakers: Marshall Williams We discuss various definitions for Quasiregular mappings in metric measure spaces. Quasiregular maps, or mappings of bounded distortion, are defined as non-homeomorphic quasiconformal mappings, much like analytic functions in the complex plane can be defined as non-homeomorphic conformal mappings. Quasiregular mappings in Euclidean space were introduced by Reshetyak in the late 60’s, and were later generalized to Carnot groups by Vodop’yanov. Very recently, there have been further generalizations; Onninen and Rajala studied quasiregular mappings from Euclidean space into certain cohomology manifolds, while Cristea considered a broad class of metric spaces. I will discuss a number of results showing new equivalences between different definitions, providing a somewhat more complete picture of the latter setting. Updated on Dec 09, 2011 05:16 AM PST 466. # Analysis on the Grushin plane: Lipschitz and quasiconformal maps Location: MSRI: Simons Auditorium Speakers: William Paul Meyerson The Grushin plane can be thought of as a two-dimensional Euclidean plane with a metric that “blows up” near the vertical axis. This gives the vertical axis a Hausdorff dimension of two. We begin by introducing the Grushin plane and discuss some basic properties. Then, we discuss a counterexample to show how analysis on the Grushin plane differs from Euclidean analysis. After that, we construct a quasiconformal map from the Grushin plane to the Euclidean plane. We finish by generalizing the Grushin plane slightly and explaining how the Grushin plane can serve as an intermediary in dealing with quasiconformal maps on Euclidean spaces. Updated on Nov 21, 2011 06:32 AM PST 467. # Compression bounds for wreath products Location: MSRI: Simons Auditorium Speakers: Sean Li The Hilbert compression exponent of a finitely generated group is the best Holder exponent lower bound for the class of Lipschitz embeddings of G into Hilbert space. We show that if G and H are finitely generated groups whose Hilbert compression exponent is positive, then so is the Hilbert compression exponent of the wreath product G ≀ H. Updated on Nov 21, 2011 06:29 AM PST 468. # Lemma Poincaré for L_infty - forms Location: MSRI: Simons Auditorium Speakers: Stanislav Dubrovskiy We show that every closed$L_infty,loc$- form on R^n is exact. Differential is understood in the sense of currents. The proof does not use any explicit geometric constructions. De Rham theorem follows. This is a joint work with Vladimir Goldshtein. Updated on Nov 22, 2011 05:43 AM PST 469. # The Second Law of Probability: Entropy Growth in the Central Limit Theorem Location: UC Berkeley, 60 Evans Hall Speakers: Keith Ball This talk will explain how a geometric principle led to the solution of a 50 year old problem: to prove an analogue of the second law of thermodynamics for the central limit process. Updated on Oct 13, 2011 10:58 AM PDT 470. # Geometry of the space of probability measures Location: MSRI: Simons Auditorium Speakers: John Lott (University of California, Berkeley) The Wasserstein space of a compact metric space X is the space of Borel probability measures P(X), equipped with a certain metric W_2. This metric comes from the problem of how to optimally transport mass on X. If X is equipped with additional structure then the Wasserstein space inherits additional structure as well. I will give a historical introduction to these ideas and indicate why they are relevant to Riemannian geometry. Updated on Dec 10, 2013 02:55 PM PST 471. # Embeddings results for geodesic manifolds Location: MSRI: Simons Auditorium Speakers: Enrico Le Donne In this talk we deal with embedding results for geodesic metric spaces that are homeomorphic to manifolds. I will give an introduction to the subRiemannian Heisenberg structure on R^3. Such a metric space is not biLipschitz embeddable into any Euclidean space. However, it can be embedded into R^4 preserving the length of all the curves. If time permits, I will discuss more general metrics. Updated on Nov 10, 2011 05:12 AM PST 472. # Postdoc Seminar Location: MSRI: Simons Auditorium Speakers: Marshall Williams Created on Nov 10, 2011 05:13 AM PST 473. # Geodesics in the Heisenberg group Location: MSRI: Simons Auditorium Speakers: Moon Duchin (Tufts University) Pansu\'s thesis identifies the kinds of metrics one can get as asymptotic cones of word metrics on nilpotent groups, and Breuillard\'s work both extends this to more kinds of groups and gives very concrete geometric descriptions of the shape of large balls and spheres, with numerous applications. I\'ll describe joint work with Christopher Mooney in which we push forward these explicit descriptions finely enough to understand the dependence on generators in the special case of the 3D Heisenberg group. We give applications to classifying geodesics in CC metrics and in word metrics, and to asymptotic density problems in the discrete and real Heisenberg group. Updated on Sep 05, 2013 02:38 PM PDT 474. # Sphere packings and the space of high-dimensional lattices Location: MSRI: Simons Auditorium Speakers: Akshay Venkatesh I will describe some modest improvements in the lower bound for high-dimensional sphere packings, and related questions about the "shape" of the space of lattices in R^N, when N is large. Created on Oct 31, 2011 02:54 AM PDT 475. # A self-dual polar decomposition for vector fields Location: MSRI: Simons Auditorium Speakers: Nassif Ghoussoub I shall explain how any non-degenerate vector field on a bounded domain of$R^n$is monotone modulo a measure preserving involution$S$(i.e.,$S^2=Identity$). This is to be compared to Brenier\'s polar decomposition which yields that any such vector field is the gradient of a convex function (i.e., cyclically monotone) modulo a measure preserving transformation. Connections to mass transport --which is at the heart of Brenier\'s decomposition-- is elucidated. This is joint work with A. Momeni. Updated on Oct 14, 2011 03:58 AM PDT 476. # A Whitney Extension Theorem for Sobolev spaces Location: MSRI: Simons Auditorium Speakers: Arie Israel We will recall classical results in smooth extension theory discovered by Hassler Whitney in the 1930\'s and present the recent construction of a linear extension operator for functions in the Sobolev space$L^{m,p}(R^n)$; that is, a linear operator that takes a real-valued function f defined on a finite subset E of Euclidean space, and produces a function F defined on$R^n$, which matches f on E, and has Sobolev norm minimal to within a factor of$C=C(m,n,p)$. This generalizes work of C. Fefferman on the extension of$C^m$functions, and in fact our method gives a new proof of his theorem. Furthermore, a closer analysis of our construction shows that the extension F can be taken to have a simple dependence on f (assisted bounded depth) though, in general, not an even simpler one (bounded depth). This is joint work with C. Fefferman and G.K. Luli. Updated on Nov 03, 2011 04:44 AM PDT 477. # Some results on Hyperbolic Reflection Groups Location: MSRI: Simons Auditorium Speakers: John Mcleod I will present some new examples of hyperbolic reflection groups arising from the quadratic forms -3x_0^2 + x_1^2 + ... + x_n^2 for n <= 13, and demonstrate that in higher dimensions this quadratic form is not reflective. Updated on Nov 03, 2011 04:43 AM PDT 478. # Mean curvature flow Location: UC Berkeley, 60 Evans Hall Speakers: Tobias Colding Mean curvature flow is the negative gradient flow of volume, so any hypersurface flows through hypersurfaces in the direction of steepest descent for volume and eventually becomes extinct in finite time. Before it becomes extinct, topological changes can occur as it goes through singularities. Thus, in some sense, the topology is encoded in the singularities. In this lecture I will discuss new and old results about singularities of mean curvature flow focusing on very results about generic singularities. Updated on Sep 18, 2013 03:09 PM PDT 479. # Finiteness theorems for arithmetic manifolds of bounded volume. Location: MSRI: Simons Auditorium Speakers: Mikhail Belolipetsky I will give a survey of some recent work on covolumes of arithmetic subgroups and corresponding locally symmetric spaces with a special emphasis on effective results. Created on Oct 31, 2011 02:55 AM PDT 480. # A subelliptic divergence-curl inequality Location: MSRI: Simons Auditorium Speakers: Yi Wang (Stanford University) In this talk, I will talk about the approximation of non-isotropic$\dot{NL}^{1,Q}$functions by$L^\infty$functions on stratified homogeneous groups, generalizing a result of Bourgain-Brezis. I will then present some applications of this result, including how to derive a divergence-curl inequality for$\bar{\partial}_b$on Heisenberg group$H^n$. This is a joint work with Po-Lam Yung. Updated on Nov 07, 2013 11:16 PM PST 481. # Assouad-Nagata dimension of connected Lie groups Location: MSRI: Simons Auditorium Speakers: Irine Peng The asymptotic Assouad-Nagata dimension is a linear version of the asymptotic dimension, and seems to carry more restrictions than other variants of large scale dimensions. By chasing the whereabouts of compact subgroups, we show that the asymptotic Assouad-Nagata dimension of a connected lie group G is the topological dimension of G/K, where K is a maximal compact subgroup of G. All contents are joint work with Jose Higes. Updated on Oct 20, 2011 02:40 PM PDT 482. # "Tensor products" between metric spaces and Banach spaces Location: MSRI: Simons Auditorium Speakers: Javier Chavez Dominguez It is generally very fruitful to identify systematically the dual norm of a given norm on a space. For some operator ideals of linear mappings between Banach spaces, the identification of the dual norm is naturally given as a norm on a tensor product of Banach spaces. When these operator ideals of linear mappings between Banach spaces are generalized to Lipschitz mappings between a metric space and a Banach space, one would still like to identify the dual spaces but the tensor product arguments do not immediately make sense. In this talk we introduce a concept that plays the role of a tensor product between a metric space and a Banach space (inspired by work of Arens and Eells in the 50's), which allows us to transfer the duality arguments to this partially non-linear situation. Created on Oct 20, 2011 03:35 AM PDT 483. # Differentiation at large scales Location: UC Berkeley, 60 Evans Hall Speakers: Irine Peng The usual notion of differentiation is a way of understanding the infinitesimal behaviour of a map, i.e. the map restricted to ever decreasing scales. However there are elements of the differentiation process that make sense at larger scales as well. I will discuss the utility of this view point in the work of Eskin-Fisher-Whyte on quasi-isometries of the 3 dimensional solvable group and some subsequent generalization. Updated on Oct 13, 2011 10:54 AM PDT 484. # An elementary introduction to monotone transportation Location: MSRI: Simons Auditorium Speakers: Keith Ball (University College) The talk will describe the classical transportation problem and the Brenier map which solves it for the most natural cost function. This map has applications in PDE, harmonic analysis, geometry and probability theory. I will explain a very elementary construction of the map and illustrate why it is so useful with an example of a deviation inequality relating transportation cost and entropy. Updated on Sep 04, 2013 12:05 PM PDT 485. # Uniqueness of Self-similar Shrinkers under Mean Curvature Flow Location: MSRI: Baker Board Room Speakers: Lu Wang In this talk, we discuss the uniqueness for smooth properly embedded self-shrinking ends in$\mathbb{R}^{n+1}$that are asymptotic to any given regular cone$C$. As an application, we prove that not every regular cone with vertex at the origin has a smooth complete properly embedded self-shrinker asymptotic to it. Updated on Oct 06, 2011 01:56 AM PDT 486. # Dynamical Studies of Euclidean Minima Location: MSRI: Baker Board Room Speakers: Zhiren Wang The Euclidean minimum is a numerical indicator that detects whether there is an Euclidean algorithm in a number field with respect to its algebraic norm. In this talk, we will briefly survey the history of its studies, in particular Cerri's work and his algorithm for the computation of Euclidean minima. Then we will discuss how facts from dynamical systems can be applied to show computability in finite time for all fields of degree 7 or higher and to produce computational complexity bounds for most fields. The talk will be based on recent joint works with Uri Shapira, as well as on previous works with Elon Lindenstrauss. No number-theoretic background is required. Updated on Oct 06, 2011 01:56 AM PDT 487. # Random walk on the torus Location: MSRI: Baker Board Room Speakers: Yves Benoist Let A and B be two-by-two volume preserving matrices with integer coefficients spanning a non-solvable group. Let x be an irrational point on the 2-torus. We toss A or B, apply it to x, get another irrational point y, do it again to y, get a point z, and again... We prove that this random trajectory is almost surely equidistributed. This is a joint work with JFQuint. Updated on Dec 10, 2013 03:04 PM PST 488. # Soficity and Cremona groups Location: MSRI: Baker Board Room Speakers: Yves Cornulier The Cremona group is the group of birational transformations of the affine space. I\'ll show that this group is sofic, and introduce the notion of sofic profile, in connection to the more classical isoperimetric profile. I\'ll define all these notions; no prerequisites are needed." Updated on Oct 06, 2011 01:53 AM PDT 489. # Dimension reduction in discrete metric geometry Location: UC Berkeley, 60 Evans Hall Speakers: William Johnson Updated on Oct 03, 2011 11:11 AM PDT 490. # The Dehn function of SL(n;Z) Location: MSRI: Baker Board Room Speakers: robert young The Dehn function is a group invariant which connects geometric and combinatorial group theory; it measures both the difficulty of the word problem and the area necessary to fill a closed curve in an associated space with a disc. The behavior of the Dehn function for high-rank lattices in high-rank symmetric spaces has long been an open question; one particularly interesting case is SL(n;Z). Thurston conjectured that SL(n;Z) has a quadratic Dehn function when n >= 4. This differs from the behavior for n = 2 (when the Dehn function is linear) and for n = 3 (when it is exponential). I have proved Thurston\'s conjecture when n >= 5, and in this talk, I will discuss some of the background of the problem and give a sketch of the proof. Updated on Oct 06, 2011 01:52 AM PDT 491. # Rigidity of quasiisometries and quasisymmetric maps Location: MSRI: Simons Auditorium Speakers: Xiangdong Xie We show that quasiisometries between many negatively curved solvable Lie groups are rigid: they preserve distance up to an additive constant. This is equivalent to the statement that quasisymmetric maps on the ideal boundary are biLipschitz. The ideal boundary of these solvable Lie groups are nilpotent Lie groups with (nonstandard) homogeneous metrics. Updated on Oct 03, 2011 09:50 AM PDT 492. # Focal hyperbolic groups, contracting automorphisms and amenability (2) Location: MSRI: Simons Auditorium Speakers: Yves Cornulier, Romain Tessera In the discrete setting, amenable hyperbolic groups are virtually cyclic, but in the locally compact setting, it is a much wider and more interesting class. In a joint work with Caprace and Monod, we give a structural characterization of amenable hyperbolic locally compact groups, in terms of contracting automorphisms of locally compact groups. If time permits, we\'ll indicate how L^p-cohomology provides some partial results about the QI classification of these groups. The talk will start at an elementary level. Updated on Oct 03, 2011 09:48 AM PDT 493. # Focal hyperbolic groups, contracting automorphisms and amenability (1) Location: MSRI: Simons Auditorium Speakers: Yves Cornulier, Romain Tessera In the discrete setting, amenable hyperbolic groups are virtually cyclic, but in the locally compact setting, it is a much wider and more interesting class. In a joint work with Caprace and Monod, we give a structural characterization of amenable hyperbolic locally compact groups, in terms of contracting automorphisms of locally compact groups. If time permits, we\'ll indicate how L^p-cohomology provides some partial results about the QI classification of these groups. The talk will start at an elementary level. Updated on Oct 03, 2011 09:47 AM PDT 494. # Norms on homology and stable length of commutators Location: MSRI: Simons Auditorium Speakers: Christophe Pittet Updated on Oct 04, 2011 10:36 AM PDT 495. # Mirror symmetry for open Riemann surfaces Location: MSRI: Simons Auditorium Speakers: Denis Auroux - University of California, Berkeley The goal of this mostly introductory talk will be to illustrate some key concepts in mirror symmetry, by considering some of the simplest examples: Riemann surfaces of low genus. These examples will be a pretext to discuss the Strominger-Yau-Zaslow picture of mirror symmetry (according to which mirror pairs carry dual torus fibrations), as well as Kontsevich\'s homological mirror symmetry conjecture. I will also try to motivate the appearance of "wrapped" Fukaya categories in the open case. Updated on Sep 30, 2011 04:27 AM PDT 496. # Random permutations and convex chains Location: MSRI: Simons Auditorium Speakers: Gergely Ambrus (Hungarian Academy of Sciences (MTA)) A classical problem in probability, that emerged in the 1970\'s, is to describe the behaviour of the length of the longest increasing subsequence in a random permutation. By now, this task has been fully accomplished: not only the expectation and the variance is known, but also the properly scaled limit distribution has been determined. Geometrically, the question can be formulated as follows: given n independent, uniform random points in the unit square, find the longest increasing chain (polygonal path through the given points) connecting two diagonally opposite corner of the square, where "length" means the number of points on the chain. The variant of the problem treated in the talk asks for the length of the longest convex chain. We determine the asymptotic expectation up to a constant factor, and derive strong concentration results. This is a joint work with Imre Barany. Updated on Sep 30, 2011 04:18 AM PDT 497. # The rate of escape for random walks on some polycyclic and abelian-by-cyclic groups Location: MSRI: Simons Auditorium Speakers: Russell Thompson We provide some background on the rate of escape of random walks and its relation to compression exponents. We then show that any simple symmetric random walk on a Cayley graph of a polycyclic group has the same rate of escape as a random walk on the integer lattice so long as the Fitting subgroup has uniform exponential distortion. The ideas behind this proof can be generalized to metabelian groups which contain non-finitely generated subgroups, where a similar result is obtained. Updated on Sep 30, 2011 04:17 AM PDT 498. # Geometric Derandomization Location: MSRI: Simons Auditorium Speakers: Adam Klivans I\'ll discuss some recent work on building pseudorandom generators for geometric concept classes. Connections to limit theorems will be discussed. No background is required. Updated on Sep 30, 2011 04:19 AM PDT 499. # RD in higher rank Location: MSRI: Simons Auditorium Speakers: Irine Peng The property or Rapid Decay is a a property of the convolution operator on the L_2 space of a finitely generated group. Valette had conjectured that all cocompact lattices in the isometry group of symmetric spaces had property RD but progress in higher ranks seems a bit limited. I will describe a different approach to the problem (via a representation on the Furstenberg boundary) that may circumvent the issues with existing approaches. All contents are joint work with Chris Connell. Updated on Sep 30, 2011 04:22 AM PDT 500. # Poincare inequalities, rigid groups and applications Location: MSRI: Simons Auditorium Speakers: Piotr Nowak A locally compact group G has Kazhdan\'s property (T) if every action of G by affine isometries on a Hilbert space has a fixed point. In this talk we will be interested in strengthening this property by replacing the Hilbert space by other Banach spaces. In particular, we will show how to generalize the geometric/spectral method for proving property (T) to the setting of reflexive Banach spaces. We will also discuss examples and present several applications. Updated on Sep 30, 2011 04:20 AM PDT 501. # Recent work on the Propeller Conjecture Location: MSRI: Simons Auditorium Speakers: Steve Heilman (joint work with Aukosh Jagannath and Assaf Naor.) How can one prove a sharp inequality? Symmetrization, Fourier analysis, and probability are often used, and we will survey some of these methods through examples. Within this context, we then survey sharp constants in Grothendieck inequalities, leading to some recent work on computing the best constant for a Grothendieck-type inequality of Khot and Naor. Updated on Sep 23, 2011 01:45 AM PDT 502. # Lattes maps and combinatorial expansion Location: MSRI: Simons Auditorium Speakers: Qian Yin We characterize Lattes maps by their combinatorial expansion behavior, and deduce new necessary and sufficient conditions for a Thurston map to be topologically conjugate to a Lattes map. In the Sullivan dictionary, this characterization corresponds to Hamenstadt\'s entropy rigidity theorem. Updated on Sep 23, 2011 01:56 AM PDT 503. # Tardos and Moser meet Lovasz Location: MSRI: Simons Auditorium Speakers: Mario Szegedy Rutgers Lovasz\\'s Local Lemma (LLL) finds a wide variety of applications in combinatorics and computer science. It allows to deduce the existence of a global solution for any system of constraints, whose variable set has intersection graph G, as long as the probability that any given constraint is not satisfied is below a threshold that depends only on the maximal degree of G. Beck has turned Lovasz\\'s existence proof into an algorithm, but with a weaker dependence on the max degree. Following several improvements Moser, and Moser and Tardos have developed a very simple algorithm, which is also optimal, when the degree tends to infinity. Their analysis reaches a certain natural bound (in terms of the entire G) with which the lemma was stated in the original paper of Lovasz. In the lemma, as stated by Lovasz, the events are not necessarily defined via an intersection graph for a family of constraints, but rather by a graph G that describes dependencies. For a fixed dependency graph G, the exact criterion under which the general LLL applies, is given by Shearer. We show that the analysis of the MT algorithm can be improved all the way to Shearer\\'s bound. In particular, whenever the probabilities are 1-epsilon factor within Shearer\\'s bound, the Moser-Tardos algorithm runs in expected time at most n /epsilon. This makes the efficient version an exact match to the non-efficient one. We also give a deeper reason for this co-incidence: A variant of the Moser-Tardos argument can actually prove the general LLL. Finally, we show that variable framework represents a real restriction. The LLL bound for the variable version for some G is higher than for the general version. This, of course, raises the question if the MT algorithm can efficiently achieve this higher bound. Joint work with Kashyap Kolipaka Updated on Sep 23, 2011 01:48 AM PDT 504. # Simple connectivity is complicated: an introduction to the Dehn function Location: UC Berkeley, 60 Evans Hall Speakers: Robert Young A lot of good math starts by taking an existence theorem and asking How many?'' or How big?'' or How fast''. The best-known example may be the Riemann hypothesis. Euclid proved that infinitely many primes exist, and the Riemann hypothesis describes how quickly they grow. I'll discuss what happens when you apply the same idea to simple connectivity. In a simply-connected space, any closed curve is the boundary of some disc, but how big is that disc? And what can that tell you about the geometry of the space? Updated on Sep 16, 2011 03:44 AM PDT 505. # An introduction to the Hanna Neumann Conjecture Location: MSRI: Simons Auditorium Speakers: Igor Mineyev The Hanna Neumann Conjecture from 1956-1957 asserts a specific upper bound on the rank of the intersection of two finitely generated subgroups in a free group. Walter Neumann proposed a strengthened version of the Hanna Neumann Conjecture (SHNC) in 1989-1990. We will present several points of view of SHNC and sketch its proof in two languages: graph theoretic and analytic. (In case you miss this talk, two talks on SHNC will be given at UC Berkeley on October 5.) Updated on Sep 23, 2011 01:47 AM PDT 506. # Invariant random subgroups and Benjamini-Schramm convergence Location: MSRI: Simons Auditorium Speakers: Miklós Abért (Hungarian Academy of Sciences (MTA)) An invariant random subgroup (IRS) of a group is a random subgroup with a conjugacy-invariant distribution. IRS-es can be used to encode the stabilizer structure of measure preserving actions and in many senses, they tend to behave like normal subgroups. On the other hand, they also carry geometric information and weak convergence of IRS-es translates to a stochastic sampling convergence that has been introduced by Benjamini and Schramm for finite graphs. In the talk I will introduce IRS-es and present recent results. Updated on Sep 14, 2011 04:18 AM PDT 507. # Quantitative Implicit Function and Extension Theorems for Lipschitz Maps. Location: MSRI: Simons Auditorium Speakers: Jonas Azzam We discuss recent work with Raanan Schul. All Lipschitz maps from$R^7$to$R^3$are orthogonal projections". This is of course quite false as stated. There is, however, a surprising grain of truth in this statement. We show that all Lipschitz maps$f:R^{n+m}\rightarrow R^{n}$can be precomposed with a bi-Lipschitz map$g:R^{n+m}\to R^{n+m}$such that$f\circ g$will satisfy, when we write the domain as$R^n\times R^m$and restrict to a large subset$E$, that$f\circ g$will be constant in the first coordinate and bi-Lipschitz in the second coordinate. Geometrically speaking, the map$g$distorts$R^7$in a controlled manner, so that the fibers of$f$are straightened out. Moreover, the target space can be replaced by any metric space. Our results are quantitative. The size of the set$E$is an important part of the discussion, and examples such as Kaufman\\'s 1979 construction of a singular map of$[0,1]^3$onto$[0,1]^2$are motivation for our estimates. On route we will discuss an extension theorem which is used to construct the bi-Lipschitz map$g$. We show that for any$f:[0,1]^{n}\rightarrow R^{D}$whose image has positive content, one may extend$f$from a large subset of its domain to a global bi-Lipschitz map$F:R^{n}\rightarrow R^{D}$. Updated on Sep 08, 2011 09:13 AM PDT 508. # Controlled coarse homology and isoperimetric inequalities Location: MSRI: Simons Auditorium Speakers: Piotr Nowak In this talk we will study a controlled coarse homology theory on finitely generated groups and vanishing of a particular "fundamental class" in the 0th homology group. We will show that on any group one needs at most linear control to kill the fundamental class and that this vanishing is characterized by a certain isoperimetric inequality on the group. We will also use invariants like type of asymptotic dimension, isoperimetric profile, isodiametric profile and decay of the heat kernel to estimate the growth necessary to kill the fundamental class. As applications we show a link with growth of primitives of volume forms on open Riemannian manifolds and make a connection to weighted Poincare inequalities studied in the context of rigidity by P.Li and J.Wang. This is joint work with Jan Spakula (University of Muenster) Updated on Sep 09, 2011 06:34 AM PDT 509. # Dvoretsky\\'s Theorem Location: MSRI: Simons Auditorium Speakers: Gideon Schechtman (Weizmann Institute of Science) Gideon will explain Dvoretsky\'s theorem and some of the ideas that surround and stem from this cornerstone of asymptotic geometric analysis. Updated on Sep 12, 2013 10:45 AM PDT 510. # Contracting the boundary of a Riemannian 2-disc Location: MSRI: Simons Auditorium Speakers: Alexander Nabutovsky Let D be a two-dimensional Riemannian disc. Denote its diameter by d, its area by A, and the length of its boundary by L. We demonstrate that the boundary of D can be contracted to a point through closed curves of length less than 2d+4L+10000\sqrt(A) answering an old question due to M. Gromov, S. Frankel and M. Katz. We are also going to discuss several simply looking related problems that we do not know how to solve. (Joint work with Y. Liokumovich and R. Rotman). Updated on Sep 08, 2011 09:08 AM PDT 511. # Graph Sparsification Location: UC Berkeley, 60 Evans Hall Speakers: Nikhil Srivastava We consider the following type of question: given a finite graph with nonnegative weights on the edges, is there a sparse graph on the same set of vertices (i.e., a graph with very few edges) which preserves the geometry of G? The answer of course depends on what we mean by preserves and geometry. It turns out that if we are interested in preserving (1) pairwise distances between all pairs of vertices or (2) weights of boundaries of all subsets of vertices, then the answer is always yes in a certain strong sense: every graph on n vertices admits a sparse approximation with O(nlogn) or O(n) edges. We discuss some of the ideas around the proof of (2), which turns out to be a special case of a more general theorem regarding matrices. The original motivation for this problem was in the design of fast algorithms for solving linear equations, but lately the ideas have found other uses, for instance in metric embeddings and probability. Joint work with J. Batson and D. Spielman. Updated on Sep 02, 2011 02:45 AM PDT 512. # Short geodesic segments on closed Riemannian manifolds Location: MSRI: Simons Auditorium Speakers: Regina Rotman A well-known result of J. P. Serre states that for an arbitrary pair of points on a closed Riemannian manifold there exist infinitely many geodesics connecting these points. A natural question is whether one can estimate the length of the "k-th" geodesic in terms of the diameter of a manifold. We will demonstrate that given any pair of points p, q on a closed Riemannian manifold of dimension n and diameter d, there always exist at least k geodesics of length at most 4nk^2d connecting them. We will also demonstrate that for any two points of a manifold that is diffeomorphic to the 2-sphere there always exist at least k geodesics between them of length at most 24kd. (Joint with A. Nabutovsky) Updated on Sep 08, 2011 09:06 AM PDT 513. # Counting paths in nilpotent and solvable groups Location: MSRI: Simons Auditorium Speakers: David Fisher I will explain a few problems concerning distributions of endpoints of certain types of paths in nilpotent and solvable groups. One can think of this as looking at the distribution of a random walk at large enough finite times. I will focus on a few special cases of quite general results, just to avoid too much notation and terminology. I will also explain why these problems arise naturally in the study of quasi-isometries of solvable Lie groups. This is joint work with Irine Peng. Updated on Sep 05, 2011 02:07 PM PDT 514. # Small-Set Expansion from Local Testability: derandomizing the noisy hypercube Location: MSRI: Simons Auditorium Speakers: Parikshit Gopalan (MSR Silicon Valley) There is a well-known connection between the expansion of a graph and its second largest eigenvalue. Motivated by connections to the Unique Games Conjecture, recent research has focused on the expansion of small sets of vertices in a graph and its spectrum. A graph G is a small-set expander if sufficiently small sets in the graph have near perfect expansion. A recent result by Arora, Barak and Steurer (ABS) shows that a small-set expander cannot have too many (polynomial in |V|) large eigenvalues. The noisy hypercube shows that the number can be at least logarithmic in the |V|. ABS raise the question of determining the right bound. We show how to construct small-set expanders which have many more large eigenvalues than the noisy hypercube. Our construction draws a connection between the spectrum of the Cayley graph of a code, and the local testability of its dual code. If time permits, we will discuss some implications for algorithmic problems like Unique Games and Max-Cut. Joint work with Boaz Barak (MSR-NE), Johan Hastad (KTH), Raghu Meka (UT Austin), Prasad Raghavendra (GaTech) and David Steurer (MSR-NE). Updated on Sep 01, 2011 04:53 AM PDT 515. # Covariance Estimation for Distributions with 2+ε Moments Location: MSRI: Simons Auditorium Speakers: Nikhil Srivastava A basic question motivated by applications in statistics and convex geometry is the following: given a mean zero random vector$X$in$R^n$, how many independent samples$X_1,\ldots X_q$does it take for the empirical covariance matrix$\tilde{C}=1/q\sum_i X_iX_i^T$to converge to the actual covariance matrix$\E XX^T$? In an influential paper, M. Rudelson that if$\|X\|\le O(\sqrt{n})$a.s. and$\E XX^T=I$, then$O((n\log n)$samples suffice for an arbitrary fixed constant approximation in the operator norm. Under these very weak assumptions on$X$, this bound is tight. We show that as long as the k-dimensional marginals of$X$have bounded 2+\epsilon moments for all k\le n, the logarithmic factor is not needed and O(n) samples are enough, which is the optimal bound. Updated on Sep 01, 2011 04:57 AM PDT 516. # Sparser Johnson-Lindenstrauss Transforms Location: MSRI: Simons Auditorium Speakers: Jelani Nelson The Johnson-Lindenstrauss (JL) lemma (1984) states that any n points in d-dimensional Euclidean space can be embedded into k = O((log n)/eps^2) dimensions so that all pairwise distances are preserved up to 1+/-eps. Furthermore, this embedding can be achieved via a linear mapping. The JL lemma is a useful tool for speeding up solutions to several high-dimensional problems: closest pair, nearest neighbor, diameter, minimum spanning tree, etc. It also speeds up some clustering and string processing algorithms, reduces the amount of storage required to store a dataset, and can be used to reduce memory required for numerical linear algebra problems such as linear regression and low rank approximation. The original proofs of the JL lemma let the linear mapping be specified by a random dense k x d matrix (e.g. i.i.d. Gaussian entries). Thus, performing an embedding requires dense matrix-vector multiplication. There has been much recent work on developing distributions that allow for embedding vectors quickly, begun by the work of [Ailon, Chazelle, STOC 2006]. Unfortunately, many of the works in this direction cannot take advantage of sparsity of the vector to embed, and take Omega(d) time to embed a vector even with only one non-zero entry. This feature is particularly unfortunate in streaming applications, where a vector x receives coordinate-wise updates of the form x <-- x + v*e_i in a data stream, so that to maintain some linear embedding Sx of x we should repeatedly calculate Se_i during stream updates (note e_i has only one non-zero entry). Even aside from streaming applications, several practical situations give rise to very sparse vectors. For example, when representing a document as a bag of words, d is the size of the lexicon, and we would not expect any single document to contain anywhere near d words. In networking applications, if x_{i,j} counts bytes sent from source i to destination j in some time interval, then d is the total number of IP pairs, whereas we would not expect most pairs of IPs to communicate with each other. One way to speed up embeddings for sparse vectors is to develop distributions over linear mappings whose matrices themselves are sparse, and investigation in this direction was carried out in [Achlioptas, PODS 2001] and [Dasgupta, Kumar, Sarlos, STOC 2010]. The former work gave a distribution over embedding matrices where each column only had s = k/3 non-zero entries, and the latter where each column had only s = O~(eps^{-1}*log^2 n) non-zero entries (which is an improvement over s=k for 1/eps >> log n). In this talk, I will present two new distributions over JL embeddings which achieve the best known sparsity to date: s = O(eps^{-1}*log n). These are the first distributions to achieve o(k) non-zero entries per column regardless of how eps and n are related. This is based on joint work with Daniel Kane (Stanford). Updated on Aug 31, 2011 10:09 AM PDT 517. # Random walks in Euclidean space Location: MSRI: Simons Auditorium Speakers: Peter Varju Consider a finite set of isometries of Euclidean space. I try to understand the local distribution of the image of the origin under the product of independent random elements of this set. In the first half of the lecture, I will survey some results about random walks in compact Lie groups. Updated on Sep 01, 2011 10:22 AM PDT 518. # Quantitative Geometry Program: 5-Minute Introductions Location: MSRI: Simons Auditorium Updated on Aug 29, 2011 07:24 AM PDT 519. # Quantitative Geometry Program: 5-Minute Introductions Location: MSRI: Simons Auditorium Updated on Aug 29, 2011 07:24 AM PDT 520. # Quantitative Geometry Program: 5-Minute Introductions Location: MSRI: Simons Auditorium Updated on Aug 26, 2011 07:17 AM PDT 521. # MSRI Evans Lecture Location: UC Berkeley, 60 Evans Hall Speakers: Marianna Csornyei (University College) Differentiability of Lipschitz functions and tangents of sets Differentiability of Lipschitz functions and tangents of sets We will show how elementary product decompositions of measures can detect directionality in sets, and show how this can be used to describe non-differentiability sets of Lipschitz functions on R^n, and to understand the phenomena that occur because of behaviour of Lipschitz functions around the points of null sets. In order to prove this we will need to prove results about the geometry of sets of small Lebesgue measure: we show that sets of small measure are always contained in a "small" collection of Lipschitz surfaces. The talk is based on a joint work with G. Alberti, P. Jones and D. Preiss. Updated on Sep 18, 2013 03:19 PM PDT 522. # AS Informal Seminar Location: MSRI: Baker Board Room Speakers: Michael Rubinstein (University of Waterloo) Updated on Sep 12, 2013 08:53 AM PDT 523. # Reflections on the semester and open discussion on future projects in arithmetic statistics Location: MSRI: Baker Board Room Speakers: David Farmer Created on May 12, 2011 09:03 AM PDT 524. # AS Informal Seminar Location: MSRI: Baker Board Room Speakers: David Farmer Updated on May 18, 2011 02:02 AM PDT 525. # A two-phase problem with lower dimensional free boundary Location: MSRI: Simons Auditorium Speakers: Arshak Petrosyan (Purdue University) We will discuss an Alt-Caffarelli-Friedman type variational problem that exhibits a codimension two free boundary. We will show the optimal regularity, nondegeneracy, among other things, as well as a new phenomenon that the positive and negative phases are always separated. We will then discuss the regularity of the free boundary in dimension 3 by using Alexandrov's reflection comparison technique. Based on a joint work with Mark Allen. Updated on Sep 11, 2013 12:28 PM PDT 526. # Selection and existence of solutions for several free boundary problems Location: MSRI: Baker Board Room Speakers: Xuming Xie There are a class of physical problems that involve selection. In this class of problems, when some parameter$\epsilon$(such as surface tension ) is zero, there are a continuum set of solutions. However, as$\epsilon $is NOT zero , only a discrete set of solutions exist. In this talk, we are going to survey some rigorous results in selection and existence for several free boundary problems such as viscous fingering and dendritic crystal growth. We will explain the selection mechanism for these physical problems and how it could be applied to the related linear stability problem. Some results are joint work with Saleh Tanveer. Created on May 06, 2011 05:53 AM PDT 527. # Moments of Rankin-Selberg Convolutions and Subconvexity Location: MSRI: Baker Board Room Speakers: Roman Holowinsky Updated on May 09, 2011 09:20 AM PDT 528. # Regular Problems with Large Interactions and Free Boundary Problems Location: MSRI: Baker Board Room Speakers: Edward Dancer We consider some systems of nonlinear parabolic equations with large interactions,for example kuv where k is large.Then the limiting equation is some form of free boundary problem.What we want to do is to use results on the behaviour of the free boundary problem to obtain information about the behaviour of the dynamical system for large k. Updated on Apr 27, 2011 09:12 AM PDT 529. # Lagrangian solutions of semigeostrophic system Location: MSRI: Baker Board Room Speakers: Mikhail Feldman (University of Wisconsin) Semigeostrophic system is a model of large-scale atmospheric/ocean flows. I will discuss some results on existence of weak solutions in "dual" and "physical" spaces. Methods and tools include Monge-Kantorovich mass transport and the theory of transport equations with BV vector fields. Open problems will be also discussed. Updated on Sep 06, 2013 10:17 AM PDT 530. # Lower order terms of moments of L(1/2,chi_d) Location: MSRI: Baker Board Room Speakers: Rishikesh Let L(s,chi_d) be the L-function associated to the quadratic character chi_d. Conrey, Farmer, Keating, Rubinstein, and Snaith conjectured a formula for the asymptotics, for X large, of the moments sum_{|d| Created on May 06, 2011 06:10 AM PDT 531. # Informal study group on Low lying zeros Location: MSRI: Baker Board Room Speakers: Kaneenika Sinha Updated on Mar 30, 2011 05:52 AM PDT 532. # Towards a p-adic Cohen-Lenstra conjecture Location: MSRI: Baker Board Room Speakers: Jordan Ellenberg (University of Wisconsin) Updated on Oct 25, 2013 11:07 AM PDT 533. # Linearization methods and viscosity solutions Location: MSRI: Simons Auditorium Speakers: Lawrence Evans (University of California, Berkeley) Viscosity solution methods are very strongly based upon, and therefore seemingly limited to, maximum principle methods. It is therefore useful to try to augment these techniques with integration-by-parts and other procedures. I will discuss how to do this for (1) Hamilton-Jacobi equations with nonconvex Hamiltonians and (2) the infinity Laplacian equation. Updated on Aug 20, 2013 02:27 PM PDT 534. # Numerics for surfaces and interfaces Location: MSRI: Simons Auditorium Speakers: Charles Elliott (University of Warwick) Our goal is to formulate a methodology for solving PDEs for and on evolving surfaces. In the first part I will discuss the problem of minimizing a Helfrich (Willmore) type energy coupled to a surface Cahn Hilliard energy. This is a model for two phase biomembranes which form the boundary of a vesicle.The surface PDEs characterising a minimizer will be derived. Using gradient flow I will show how one may seek minimizers by looking for stationary solutions of a geometric fourth order evolution PDE for an evolving surface whose motion is coupled to an equation of Allen-Cahn type on that surface. One may view this as an example of a free boundary on a free boundary. In the second part I will discuss numerical methods based on phase field models and surface finite elements. In particular I will describe double obstacle phase field models and the evolving surface finite element method. Updated on Sep 06, 2013 09:26 AM PDT 535. # Period functions of Eisenstein series and cotangent sums Location: MSRI: Simons Auditorium Speakers: Sandro Bettin We consider the sum$\sum_{n=1}^\infty \sigma_a(n)e^{2\pi i nz}$, showing that its period function can be analytically continued in z and has a very fast converging Taylor series in Re(z)>0. We then use these results to deduce an exact formula for the second moment of the Riemann zeta function. Moreover, we introduce a family of cotangent sums, functions over the rationals that generalize the Dedekind sum, and share with it the property of having an "almost" analytic period function. Created on Apr 28, 2011 06:00 AM PDT 536. # Period functions of Eisenstein series and cotangent sums. Location: MSRI: Simons Auditorium Speakers: Sandro Bettin We consider the sum$\sum_{n=1}^\infty \sigma_a(n)e^{2\pi i nz}$, showing that its period function can be analytically continued in z and has a very fast converging Taylor series in Re(z)>0. We then use these results to deduce an exact formula for the second moment of the Riemann zeta function. Moreover, we introduce a family of cotangent sums, functions over the rationals that generalize the Dedekind sum, and share with it the property of having an "almost" analytic period function. Created on Apr 29, 2011 07:50 AM PDT 537. # AS PD seminar Location: MSRI: Simons Auditorium Created on Apr 29, 2011 07:52 AM PDT 538. # 2011 Serge Lang Undergraduate Lecture : "Patterns in the primes" Location: MSRI: Simons Auditorium Speakers: Andrew Granville Is there a formula for the primes? Can you identify a prime quickly if you see one? How many primes are there? (A precise enough answer to this question is worth a million dollars!) Are there magic squares of primes? What patterns can you make with primes? In this talk we will discuss these questions and many more. The speaker will be happy to try to answer any questions that members of the audience might have about primes. Updated on Apr 15, 2011 08:58 AM PDT 539. # Jumping Champions for Prime Gaps Location: MSRI: Baker Board Room Speakers: Daniel Goldston Consider the sequence of primes: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, . . . and also the differences or gaps between the consecutive primes here: 1, 2, 2, 4, 2, 4, 2, 4, 6, 2, . . . . The most common difference for primes up to x is called a jumping champion, so for example when x=11 the jumping champion is 2. For x>947 the jumping champion is always 6 at least past x= 1,000,000,000,000,000, but nothing beyond this has been proved about jumping champions. Despite this, it is conjectured that aside from 1 the jumping champions are 4 and the primorials 2, 6, 30, 210, 2310. . . . Following up on earlier work of Odlyzko, Rubinstein and Wolf, we will provide some theoretical support for this conjecture. This is joint work with Andrew Ledoan. Updated on Apr 22, 2011 09:02 AM PDT 540. # Informal study group on Low lying zeros Location: MSRI: Baker Board Room Speakers: Kaneenika Sinha Updated on Mar 30, 2011 05:52 AM PDT 541. # Undercompressible shock waves and moving phase boundaries Location: MSRI: Baker Board Room Speakers: Philippe LeFloch (Université Pierre et Marie Curie) I will discuss the existence and properties of shock wave solutions to nonlinear hyperbolic systems when certain underlying small-scales (viscosity, capillarity, etc.) determine the selection of admissible shocks. Regularization-sensitive patterns often arise in continuum physics, especially in complex fluid flows which may contain undercompressive shock waves and moving phase boundaries. The so-called kinetic relation is introduced to characterize the correct dynamics of these nonclassical waves, and is tied to a higher-order regularization that takes into account additional physics. I will discuss various techniques and results about the Riemann problem, traveling waves, Glimm-type schemes, and total variation functionals adapted to nonclassical shocks. For preprints, see: philippelefloch.wordpress.com Updated on Dec 10, 2013 10:56 AM PST 542. # Well-posedness of the two and three dimensional full water wave problem Location: MSRI: Baker Board Room Speakers: Sijue Wu (University of Michigan) In this talk, I will discuss some recent results on the local, global and almost global well-posedness of the two and three dimensional full water wave problems, and the main ideas involved in the proofs. Updated on Apr 21, 2011 09:36 AM PDT 543. # Explicit Formula Informal Study Group Location: MSRI: Baker Board Room Speakers: David Farmer Created on Apr 25, 2011 03:13 AM PDT 544. # Waves with prescribed distribution of vorticity Location: MSRI: Simons Auditorium Speakers: John Toland This concerns a variational theory of steady periodic surface waves in which the distribution function of vorticity (its rearrangement class) in the underlying flow is prescribed. Waves arise from minimizing the total energy and the functional dependence of vorticity on the stream function emerges as the Lagrange multiplier that comes from prescribing the vorticity distribution. The theory does not distinguish between irrotational waves and waves with locally square-integrable vorticity. Updated on Apr 18, 2011 02:20 AM PDT 545. # Boundary singular solutions associated with connecting thin tubes Location: UC Berkeley, 60 Evans Hall Speakers: Susanna Terracini Refreshments after lecture at La Val's Pizza. Consider two domains connected by a thin tube so that the mass of a given eigenfunction (linear or nonlinear) concentrates in only one of the two domains. The restriction on the other domain develops a singularity at the junction of the tube, as the section of the channel shrinks to zero. The asymptotics for this type of solutions can be precisely described. This is a result obtained in collaboration with L. Abatangelo and V. Felli Updated on Apr 19, 2011 04:28 AM PDT 546. # Singular Jacobi Forms of Number Fields Location: MSRI: Simons Auditorium Speakers: Hatice Boylan Updated on Apr 21, 2011 09:40 AM PDT 547. # Higher Mahler measure and Lehmer's question Location: MSRI: Simons Auditorium Speakers: Kaneenika Sinha The Mahler measure M(f) of a monic polynomial f is defined to be the absolute value of the product of those roots of f which lie outside the unit disk. The logarithmic Mahler measure m(f) = log M(f) turns out to be the integral of log|f| on the unit circle. In 1933, Lehmer essentially asked the following question: for any C >0, can we find a polynomial with integer coefficients such that 01,$ we define the k- higher Mahler measure to be the integral of log^k |f| on the unit circle. We explore the analogues of Lehmer's question for these higher Mahler measures. This is joint work with Matilde Lalin.
Created on Apr 21, 2011 09:15 AM PDT
548. # Informal study group on Low lying zeros

Location: MSRI: Baker Board Room
Speakers: Kaneenika Sinha

Updated on Mar 30, 2011 05:50 AM PDT
549. # Counting Points on Curves over Finite Fields

Location: UC Berkeley, 60 Evans Hall
Speakers: Melanie Wood

Refreshments after lecture at La Val's Pizza

Updated on Apr 05, 2011 09:14 AM PDT
550. # Computing critical values of quadratic Dirichlet L-functions, with an eye toward their moments.

Location: MSRI: Simons Auditorium
Speakers: Matthew Alderson

Moments of L-functions has been a topic of intense research in recent years. Through the integration of random matrix theory and multiple Dirichlet series with traditional number theoretic arguments, methods for studying the moments of L-functions have been developed and, in turn, have lead to many well-posed conjectures for their behavior. In my talk, I will discuss the (integral) moments of quadratic DIrichlet L-functions evaluated at the critical point s=1/2. In particular, I will present formulas for computing the critical values for such L-functions and then compare the data for the corresponding moments to the (aforementioned) conjectured moments.
Created on Apr 15, 2011 09:13 AM PDT
551. # New computations of the Riemann zeta function

Location: MSRI: Simons Auditorium
Speakers: Jonathan Bober

I'll describe the implementation of Hiary's O(t1/3) algorithm and the computations that we have been running using it. Some highlights include the 10^32nd zero (and a few hundred of its neighbors, all of which lie on the critical line), values of S(T) which are larger than 3, and values of zeta larger than 14000.
Created on Apr 15, 2011 09:11 AM PDT
552. # 2011 Chern Lectures

Location: UC Berkeley, 60 Evans Hall
Speakers: Andrei Okounkov

Updated on Apr 05, 2011 05:14 AM PDT
553. # Stokes waves among global free-boundary problems

Location: MSRI: Baker Board Room
Speakers: John Toland

The purpose of this informal introductory lecture is to observe that the study of classical Stokes-waves belong to a class of geometric problems in which zero Dirichlet conditions for a harmonic function combine with the requirement that the normal derivative is a non-constant function of position to determine the free boundary. When surface tension is included, the normal derivative is determined by the the position and a constant multiple of the boundary curvature; when the liquid is bounded by an elastic sheet the free boundary is determined by requiring that the normal derivative depends on position and nonlinearly on the curvature. In a later lecture the problem for steady waves with prescribed distribution of vorticity (prescribed rearrangement class) will be discussed. That the vorticity is a function of the stream function is the Lagrange multiplier rule corresponding to this prescription. Thus the stream function satisfies a semilinear Poisson equation in which the nonlinearity is not prescribed a priori; it is part of the solution.
Updated on Apr 11, 2011 09:06 AM PDT
554. # Geometry of non local and non local phase transitions in some geometrical frameworks

Location: MSRI: Baker Board Room
Speakers: Yannick Sire

I will describe several recent results concerning local and non local equations on euclidean space and riemannian manifolds in connection with a conjecture by De Giorgi.
Created on Apr 08, 2011 03:18 AM PDT
555. # 2011 Chern Lectures

Location: UC Berkeley

Updated on Apr 05, 2011 05:13 AM PDT
556. # Porous Medium Flows: from local to nonlocal models III

Location: MSRI: Baker Board Room
Speakers: Juan Vazquez

Updated on Apr 08, 2011 03:21 AM PDT
557. # Review and recent works on the large time asymptotics for Hamilton-Jacobi equations

Location: MSRI: Baker Board Room
Speakers: Hiroyoshi MITAKE

Created on Apr 08, 2011 06:19 AM PDT
558. # 2011 Chern Lectures

Location: UC Berkeley
Speakers: Andrei Okuonkov

Updated on Apr 05, 2011 05:12 AM PDT
559. # AS-Informal Study Group

Location: MSRI: Baker Board Room
Speakers: David Farmer

Created on Apr 05, 2011 05:19 AM PDT
560. # Central values of the symmetric square L-functions

Location: MSRI: Baker Board Room
Speakers: Wenzhi Luo

We prove a bound for the square mean of the central value of the symmetric square L-functions associated to holomorphic cusp forms, when the weight k varies in short intervals. Our approach is via Zagier's kernel function for the symmetric square L-functions.
Created on Apr 07, 2011 09:31 AM PDT
561. # Explicit Formula Seminar: "Bounds on gaps between zeros of L-functions"

Location: MSRI: Baker Board Room
Speakers: Jonathan Bober

Updated on Mar 31, 2011 04:42 AM PDT
562. # Floating Drops: a survey of problems and results, with a focus on symmetry

Location: MSRI: Simons Auditorium
Speakers: Ray Treinen

Updated on Dec 04, 2013 01:29 PM PST
563. # 2011 Chern Lectures

Location: UC Berkeley
Speakers: Andrei Okounkov

Updated on Apr 04, 2011 03:13 AM PDT
564. # Bhargava-Shankar informal study group: Square-free values of discriminant polynomials.

Location: MSRI: Simons Auditorium
Speakers: Manjul Bhargava

Updated on Mar 31, 2011 04:39 AM PDT
565. # Porous Medium Flows: from local to nonlocal models II

Location: MSRI: Simons Auditorium
Speakers: Juan Vazquez

Updated on Mar 31, 2011 04:38 AM PDT
566. # Moment Polynomials for the Riemann Zeta Function

Location: MSRI: Simons Auditorium
Speakers: Shuntaro Yamagishi

I will explain how we calculated the coefficients of moment
polynomials for the Riemann zeta function for k = 4,5.., 13
and numerically tested them against the moment polynomial conjecture.
Updated on Mar 31, 2011 04:37 AM PDT
567. # FBP-Informal Seminar

Location: MSRI: Baker Board Room
Speakers: TBA, Lihe Wang

Updated on Apr 01, 2011 03:03 AM PDT
568. # Averages of central L-values

Location: MSRI: Simons Auditorium
Speakers: TBA

Updated on Apr 01, 2011 08:17 AM PDT
569. # Non-Degeneracy of an Elliptic-Free Boundary Problem

Location: MSRI: Simons Auditorium
Speakers: Betul Orcan (University of Texas)

In this talk, we will consider a free boundary problem with a
very general free boundary condition and analyze the non-degeneracy of the
largest subsolution near the free boundary.
Updated on Mar 31, 2011 04:36 AM PDT
570. # Bay Area Algebraic Number Theory and Arithmetic Geometry Day II

Location: UC Berkeley, 60 Evans Hall

Updated on Mar 25, 2011 04:26 AM PDT
571. # Bhargava-Shankar informal study group: Square-free values of discriminant polynomials.

Location: MSRI: Simons Auditorium
Speakers: Manjul Bhargava

Updated on Mar 25, 2011 06:19 AM PDT
572. # Porous Medium Flows: from local to nonlocal models

Location: MSRI: Simons Auditorium
Speakers: Juan Vazquez

Updated on Mar 18, 2011 02:45 AM PDT
573. # Linearization Techniques in Free Boundary Problems

Location: UC Berkeley, 60 Evans Hall

Refreshments after lecture at La Val\\\\\\'s Pizza.

Updated on Mar 17, 2011 04:25 AM PDT
574. # "Computing L-functions in SAGE"

Location: MSRI: Simons Auditorium
Speakers: Rishikesh

Created on Mar 23, 2011 08:26 AM PDT
575. # Asymptotics for the coefficients of Kac-Wakimoto characters

Location: MSRI: Simons Auditorium
Speakers: Karl Mahlburg

Updated on Mar 25, 2011 06:40 AM PDT
576. # Postdoctoral Seminar FBP-TBA

Location: MSRI: Simons Auditorium

Created on Mar 25, 2011 06:05 AM PDT
577. # Informal study group on Low lying zeros: Alternatives to Dirichlet Series Amplifiers

Location: MSRI: Simons Auditorium

Updated on Mar 18, 2011 09:19 AM PDT
578. # A Short Introduction to Free-boundary Problems for Incompressible and Compressible Fluid Dynamics

Location: MSRI: Simons Auditorium
Speakers: Steve Shkoller

Updated on Mar 18, 2011 02:43 AM PDT
579. # A Short Introduction to Free-boundary Problems for Incompressible and Compressible Fluid Dynamics

Location: MSRI: Simons Auditorium
Speakers: Steve Shkoller

Updated on Mar 18, 2011 02:43 AM PDT
580. # Holder extensions and a non-local and non-linear operator.

Location: MSRI: Simons Auditorium
Speakers: Erik Lindgren

Updated on Mar 18, 2011 02:50 AM PDT
581. # Curious q-series and Jacobi Theta functions

Location: MSRI: Simons Auditorium

Updated on Mar 18, 2011 09:27 AM PDT
582. # Cohomology of Bianchi Groups and Arithmetic

Location: MSRI: Simons Auditorium
Speakers: Mehmet Sengun

Updated on Mar 07, 2011 03:28 AM PST
583. # Informal study group on Low lying zeros

Location: MSRI: Simons Auditorium
Speakers: Kaneenika Sinha

Updated on Mar 14, 2011 09:03 AM PDT
584. # Free boundary problem posed by Guy David and Calder'on--Zygmund capacities

Location: MSRI: Baker Board Room
Speakers: Alexander Volberg

Updated on Mar 14, 2011 09:02 AM PDT

Speakers: James Weigandt

Created on Mar 10, 2011 06:52 AM PST
586. # Non-linear problems involving integro-differential equations

Location: MSRI: Baker Board Room

Updated on Mar 14, 2011 09:01 AM PDT
587. # Elliptic curves, their companions, and their statistics

Location: UC Berkeley, 60 Evans Hall
Speakers: Barry Mazur (Harvard University)

Refreshments after lecture at La Val\\'s Pizza.

Updated on Dec 09, 2013 10:54 AM PST
588. # SSL group, course "Space Weather"

Group will visit the first floor terrace to catch a view of the satellite dish.

Created on Mar 10, 2011 01:27 AM PST
589. # Elliptic curves of arbitrarily large rank (Over Function Fields)

Speakers: Kevin Wilson

Updated on Mar 14, 2011 08:03 AM PDT
590. # Fun talk on high precision computation of number theoretical constants

Location: MSRI: Baker Board Room
Speakers: Henri Cohen

Updated on Mar 08, 2011 07:03 AM PST
591. # Informal study group on Low lying zeros: Analytic rank of $J_0(N)$

Location: MSRI: Baker Board Room
Speakers: Kaneenika Sinha

Updated on Mar 08, 2011 07:02 AM PST
592. # Nonlinear diffusion and free boundaries. From porous media to fractional diffusion

Location: UC Berkeley, 60 Evans Hall
Speakers: Juan Vazquez

Refreshments after lecture at La Val\\\\\\\\\\'s Pizza.

Updated on Feb 18, 2011 03:47 AM PST
593. # Empirical Evidence for an Arithmetic Analogue of Nevanlinna's Five Value Theorem

Location: MSRI: Baker Board Room
Speakers: James Weigandt

Updated on Feb 28, 2011 07:57 AM PST
594. # Newforms and multiplicities on $\Gamma_0(9)$

Location: MSRI: Baker Board Room
Speakers: Fredrik Strömberg

Updated on Mar 07, 2011 12:04 AM PST
595. # The field of Fourier coefficients of a modular form

Location: MSRI: Simons Auditorium

Updated on Feb 28, 2011 08:12 AM PST
596. # Low lying zeros: Lower order terms for the one-level density of elliptic curve L-functions

Location: MSRI: Simons Auditorium
Speakers: Duc Khiem Huynh

Updated on Feb 22, 2011 05:02 AM PST
597. # Non-linear problems involving integro-differential equations

Location: MSRI: Simons Auditorium

Updated on Feb 18, 2011 04:20 AM PST
598. # Bhargava-Shankar informal study group

Location: MSRI: Simons Auditorium
Speakers: Manjul Bhargava

Updated on Feb 15, 2011 07:12 AM PST
599. # Non-linear problems involving integro-differential equations

Location: MSRI: Simons Auditorium

Updated on Feb 18, 2011 04:19 AM PST
600. # Postdoctoral Seminar AS-TBA

Location: MSRI: Simons Auditorium
Speakers: Karl Mahlburg

Updated on Mar 25, 2011 06:03 AM PDT
601. # Postdoctoral Seminars FBP

Created on Feb 18, 2011 04:31 AM PST
602. # Low Lying zeros seminar: Petersson's formula and related topics

Speakers: Andrew Knightly

Updated on Feb 18, 2011 04:11 AM PST
603. # Free boundary problems with surface tension.

Speakers: Stephan Luckhaus

Updated on Feb 18, 2011 03:58 AM PST
604. # Free boundary problems with surface tension

Location: MSRI: Simons Auditorium
Speakers: Stephan Luckhaus

Updated on Feb 18, 2011 03:57 AM PST
605. # AS-FRG Project

Location: MSRI: Baker Board Room
Speakers: Michael Rubinstein (University of Waterloo)

Updated on Sep 12, 2013 08:53 AM PDT
606. # Informal study group on Low lying zeros

Location: MSRI: Baker Board Room
Speakers: David Farmer

Updated on Feb 13, 2011 02:49 AM PST
607. # Obstacle type problems and its ramifications

Location: MSRI: Baker Board Room
Speakers: Henrik Shahgholian

Updated on Feb 13, 2011 02:47 AM PST
608. # Informal study group for 2-Selmer

Location: MSRI: Baker Board Room
Speakers: Danial Kane (Harvard University)

Updated on Feb 13, 2011 02:45 AM PST
609. # Bhargava-Shankar informal study group

Location: MSRI: Baker Board Room
Speakers: Manjul Bhargava

Updated on Feb 13, 2011 02:43 AM PST
610. # "Shape optimization: an introduction"

Location: MSRI: Baker Board Room
Speakers: Dorin Bucur

Updated on Feb 13, 2011 02:33 AM PST
611. # The Arithmetic of Quadratic Forms

Location: UC Berkeley, 60 Evans Hall
Speakers: Jonathan Hanke

Refreshments after lecture at La Val\\\\\\'s Pizza.

Updated on Feb 13, 2011 02:31 AM PST
612. # A problem related to the ABC conjecture

Speakers: Danial Kane (Harvard University)

Updated on Feb 13, 2011 03:01 AM PST
613. # Nonlocal equations and new notions of curvature

Location: MSRI: Baker Board Room
Speakers: Nestor Guillen

Updated on Feb 13, 2011 03:00 AM PST
614. # Brandt module of ternary quadratic forms

Location: MSRI: Baker Board Room
Speakers: Gonzalo Tornaría

Updated on Feb 13, 2011 02:59 AM PST
615. # AS-FRG Project

Location: MSRI: Simons Auditorium

Updated on Jan 28, 2011 05:27 AM PST
616. # Order and Chaos

Location: MSRI: Simons Auditorium
Speakers: Carl Pomerance (Dartmouth College)

Updated on Sep 11, 2013 12:54 PM PDT
617. # Elastic Free Energies and many body Hamiltonians, covering possible phase change too.

Location: MSRI: Simons Auditorium
Speakers: Stephan Luckhaus

Updated on Feb 07, 2011 04:38 AM PST
618. # Low-Lying Zeros"

Speakers: Henryk Iwaniec

Created on Feb 07, 2011 04:39 AM PST
619. # A free boundary problem related to complex dynamics

Location: MSRI: Simons Auditorium
Speakers: Alexander Volberg

Updated on Feb 07, 2011 04:32 AM PST
620. # AS-Informal Study Group

Location: MSRI: Simons Auditorium

Updated on Jan 24, 2011 08:36 AM PST
621. # Informal reading group on the Cohen-Lenstra heuristics

Speakers: Bjorn Poonen (Massachusetts Institute of Technology)

Updated on Sep 11, 2013 12:59 PM PDT
622. # "Shape optimization: an introduction"

Location: MSRI: Simons Auditorium
Speakers: Dorin Bucur

Updated on Feb 04, 2011 05:29 AM PST
623. # MSRI-Evans Lecture- Henryk Iwaniec

Location: UC Berkeley, 60 Evans Hall
Speakers: Henryk Iwaniec

Refreshments after lecture at La Val's Pizza.

Updated on Jan 15, 2011 08:15 AM PST
624. # Regularity for Elliptic Equations with Discontinous BMO Coefficients in Reifenberg Flat Domains

Location: MSRI: Simons Auditorium

Pizza Lunch

Updated on Feb 04, 2011 05:25 AM PST
625. # "Low-lying zeros of Dedekind zeta functions"

Location: MSRI: Simons Auditorium
Speakers: Andrew Yang

Pizza Lunch

Updated on Feb 04, 2011 05:52 AM PST
626. # A factorization method for non-symmetric linear operator: enlargement of the functional space while preserving hypo-coercivity.

Location: MSRI: Baker Board Room
Speakers: Maria Pia Gualdani

Updated on Feb 01, 2011 03:49 AM PST
627. # Well-posedness of the 3-D compressible Euler equations with moving vacuum boundary

Location: MSRI: Baker Board Room
Speakers: Steve Shkoller

Updated on Jan 28, 2011 04:54 AM PST
628. # FBP-Working Seminar-TBA

Location: MSRI: Baker Board Room

Updated on Jan 24, 2011 08:27 AM PST
629. # Postdoctoral Seminars FBP

Location: MSRI: Baker Board Room

Pizza Lunch

Updated on Jan 24, 2011 08:17 AM PST
630. # "Mathematical modelling of tissue growth"

Speakers: John King

Created on Jan 24, 2011 08:50 AM PST
631. # "A variational approach to isoperimetric inequalities"

Location: MSRI: Baker Board Room
Speakers: Dorin Bucur

Updated on Jan 24, 2011 08:44 AM PST
632. # "Mathematical modelling of tissue growth"

Created on Jan 24, 2011 08:45 AM PST
633. # "5-Minute Presentations"

Pizza Lunch 12pm-1:30pm

Created on Jan 24, 2011 01:22 AM PST
634. # Arithmetic Statistics- Informal Study Group

Location: MSRI: Simons Auditorium
Speakers: Melanie Wood

Updated on Jan 24, 2011 01:18 AM PST
635. # "Cohen-Lenstra heuristics" (Informal Reading Group)

Speakers: Bjorn Poonen (Massachusetts Institute of Technology)

Updated on Sep 11, 2013 12:59 PM PDT
636. # Free Boundary Problems

Location: UC Berkeley, 60 Evans Hall
Speakers: Luis Caffarelli (University of Texas)

Refreshments after lecture at La Val\\'s Pizza.

Updated on May 15, 2013 04:46 PM PDT
637. # Inverse Problems and Applications Seminar TBA

Location: MSRI: Simons Auditorium

Updated on May 13, 2013 11:01 PM PDT
638. # Random Matrix Seminar TBA

Location: MSRI: Simons Auditorium

Updated on May 13, 2013 11:01 PM PDT
639. # Random Matrix Seminar TBA

Location: MSRI: Simons Auditorium

Updated on May 13, 2013 11:01 PM PDT
640. # Inverse Problems and Applications Seminar TBA

Location: MSRI: Simons Auditorium

Updated on May 13, 2013 11:01 PM PDT
641. # Postdoctoral and Graduate Student Seminar TBA

Location: MSRI: Simons Auditorium

Pizza Lunch

Updated on May 13, 2013 11:01 PM PDT
642. # Inverse Problems and Applications Seminar TBA

Location: MSRI: Simons Auditorium

Updated on May 13, 2013 11:01 PM PDT
643. # The d-bar approach to inverse scattering and solution of the Davey-Stewartson Equations

Location: MSRI: Baker Board Room
Speakers: Peter Perry

Updated on Dec 05, 2010 06:26 AM PST
644. # Estimates for a family of multi-linear forms and the continuity of a scattering map in two dimensions.

Location: MSRI: Baker Board Room
Speakers: Russell Brown

Updated on Dec 05, 2010 06:25 AM PST
645. # Gluing semiclassical resolvent estimates via propagation of singularities.

Location: MSRI: Baker Board Room
Speakers: Kiril Datchev

Pizza Lunch

Updated on Dec 05, 2010 06:23 AM PST
646. # New non-elliptic methods in the analysis of conformally compact (asymptotically hyperbolic) spaces

Location: MSRI: Baker Board Room
Speakers: András Vasy

Updated on Dec 05, 2010 06:22 AM PST
647. # Approximation of inverse boundary value problems by phase-field methods

Location: MSRI: Simons Auditorium
Speakers: Luca Rondi

Updated on Nov 29, 2010 03:35 AM PST
648. # Gaussian fluctuations for Plancherel partitions

Location: MSRI: Simons Auditorium
Speakers: Leonid Bogachev

Updated on Nov 29, 2010 03:34 AM PST
649. # Random sorting networks

Location: MSRI: Simons Auditorium

Updated on Nov 29, 2010 03:33 AM PST
650. # Limits of spiked random matrices

Location: MSRI: Simons Auditorium

Updated on Nov 29, 2010 03:31 AM PST
651. # Hermitian matrix models with spiked external source

Location: MSRI: Simons Auditorium
Speakers: Jinho Baik (University of Michigan)

Updated on Sep 04, 2013 11:36 AM PDT
652. # White noise approximation for propagation and imaging in random media

Location: MSRI: Simons Auditorium
Speakers: Knut Solna

Updated on Nov 29, 2010 03:27 AM PST
653. # Lower bounds for the volume of the nodal sets

Location: MSRI: Simons Auditorium
Speakers: Hamid Hezari

Pizza Lunch

Updated on Nov 29, 2010 03:26 AM PST
654. # Non-intersecting Brownian Motions at a Tacnode: Soft and Hard Edge Case.

Location: MSRI: Simons Auditorium

Pizza Lunch

Updated on Nov 29, 2010 03:22 AM PST
655. # Unique continuation problems for pde's with rough coefficients

Location: MSRI: Simons Auditorium

Updated on Nov 29, 2010 03:21 AM PST
656. # Tau functions and convolution symmetries: applications to random matrices

Location: MSRI: Simons Auditorium

Updated on Nov 19, 2010 08:28 AM PST
657. # Gibbs resampling properties: droplet boundaries, and non-intersecting diffusions

Location: UC Berkeley
Speakers: Alan Hammond

Created on Nov 19, 2010 08:30 AM PST
658. # Harmonic maps into conic surfaces with cone angles less than $2\pi$

Updated on Nov 22, 2010 03:33 AM PST
659. # A tale of two tiling problems

Speakers: Benjamin Young

Updated on May 29, 2013 09:25 AM PDT
660. # Inverse Problems and Applications Seminar TBA

Location: MSRI: Baker Board Room

Updated on May 13, 2013 11:01 PM PDT
661. # Random Matrix Seminar TBA

Location: MSRI: Baker Board Room

Updated on May 13, 2013 11:01 PM PDT
662. # Inverse Problems and Applications Seminar TBA

Location: MSRI: Baker Board Room

Updated on May 13, 2013 11:01 PM PDT
663. # Postdoctoral and Graduate Student Seminar TBA

Location: MSRI: Baker Board Room

Pizza Lunch

Updated on May 13, 2013 11:01 PM PDT
664. # Inverse Problems and Applications Seminar TBA

Location: MSRI: Baker Board Room

Updated on May 13, 2013 11:01 PM PDT
665. # Modelling the Free World

Speakers: Jonathan Novak

Updated on Dec 04, 2013 12:45 PM PST
666. # Exploring the Free World

Location: MSRI: Simons Auditorium
Speakers: Jonathan Novak

Updated on Dec 04, 2013 12:45 PM PST
667. # Discovering the Free World

Location: MSRI: Baker Board Room
Speakers: Jonathan Novak

Updated on Dec 04, 2013 12:45 PM PST
668. # Elliptic distributions on stepped surfaces and an elliptic biorthogonal ensemble

Location: MSRI: Baker Board Room

Updated on Nov 05, 2010 04:14 AM PDT
669. # Dihedral symmetry and the Razumov-Stroganov Ex-Conjecture

Location: MSRI: Baker Board Room

Pizza Lunch

Updated on Nov 05, 2010 07:12 AM PDT
670. # Tunnel effect and symmetries for Kramers-Fokker-Planck type operators

Location: MSRI: Simons Auditorium

Updated on Oct 29, 2010 05:43 AM PDT
671. # Two groups of non-colliding Brownian motions

Location: MSRI: Simons Auditorium
Speakers: Kurt Johansson

Updated on Oct 29, 2010 05:54 AM PDT
672. # "Random matrix perturbations and quantization of tori"

Location: MSRI: Simons Auditorium
Speakers: Maciej Zworski (University of California, Berkeley)

Updated on Sep 10, 2013 04:01 PM PDT
673. # Inversion of the Born Series in Optical Tomography

Location: MSRI: Simons Auditorium
Speakers: John Schotland

Updated on Oct 29, 2010 05:26 AM PDT
674. # Random Matrix Seminar TBA

Location: MSRI: Simons Auditorium

Updated on May 13, 2013 11:01 PM PDT
675. # Inverse Problems for Classical and Quantum Random Walks

Location: MSRI: Simons Auditorium
Speakers: Alberto Ruiz Gonzalez

Updated on Oct 11, 2010 03:29 AM PDT
676. # Inverse Problems and Applications Seminar TBA

Location: MSRI: Simons Auditorium

Updated on May 13, 2013 11:01 PM PDT
677. # "The Kardar-Parisi-Zhang Equation: The free energy of the continuum random polymer."

Location: UC Berkeley
Speakers: Ivan Corwin (Columbia University)

Updated on Oct 17, 2013 06:10 PM PDT
678. # Geometric structures in the study of the geodesic ray transform

Location: MSRI: Simons Auditorium
Speakers: Juha-Matti Perkkio

Pizza Lunch

Updated on Oct 29, 2010 06:27 AM PDT
679. # "Edge scaling limits for non-Hermitian random matrices"

Location: MSRI: Simons Auditorium
Speakers: Martin Bender

Updated on Oct 29, 2010 07:57 AM PDT
680. # Postdoctoral and Graduate Student Seminar TBA

Location: MSRI: Simons Auditorium

Pizza Lunch

Updated on May 13, 2013 11:01 PM PDT
681. # New reconstruction formulas and algorithms for problems of thermoacoustic tomography

Location: MSRI: Simons Auditorium
Speakers: Leonid Kunyansky

Updated on Oct 29, 2010 04:25 AM PDT
682. # Local and Global Injectivity for Weighted Radon Transforms"

Location: MSRI: Baker Board Room
Speakers: Jan Boman

Updated on Oct 23, 2010 04:06 AM PDT
683. # Support Convergence in the Single Ring Theorem

Location: MSRI: Baker Board Room
Speakers: Ofer Zeitouni (University of Minnesota Twin Cities)

Updated on Sep 11, 2013 09:18 AM PDT
684. # "Support Convergence in the Single Ring Theorem"

Location: MSRI: Baker Board Room
Speakers: Ofer Zeitouni (University of Minnesota Twin Cities)

Updated on Sep 11, 2013 09:18 AM PDT
685. # Discussion on RMT Community Server

Created on Oct 23, 2010 05:30 AM PDT
686. # "From Random Tilings to Representation Theory"

Location: MSRI: Baker Board Room

Updated on Oct 23, 2010 05:18 AM PDT
687. # "Seismic Inverse Scattering by Reverse Time Migration"

Location: MSRI: Baker Board Room
Speakers: Christiaan Stolk

Updated on Oct 23, 2010 04:04 AM PDT
688. # The Kardar-Parisi-Zhang Equation: Deriving the Exact One-point Function Formula.

Location: UC Berkeley
Speakers: Ivan Corwin (Columbia University)

Updated on Oct 17, 2013 06:10 PM PDT
689. # From Oscillatory Integrals to a Cubic Random Matrix Model"

Speakers: Alfredo Deaño

Pizza Lunch

Updated on Oct 23, 2010 05:07 AM PDT
690. # Shear Wave Speed Recovery in Crawling Wave Sonoelastography

Pizza Lunch

Updated on Oct 23, 2010 05:12 AM PDT
691. # Fast Multiscale Gaussian Wavepacket Transforms and Multiscale Gaussian Beams for the Wave Equation

Location: MSRI: Baker Board Room
Speakers: Jianliang Qian

Updated on Oct 23, 2010 04:01 AM PDT
692. # Partial Data for General Second Order Elliptic Operators in Two Dimensions

Location: MSRI: Simons Auditorium
Speakers: Oleg Emanouilov (Imanuvilov)

Updated on Oct 16, 2010 06:14 AM PDT
693. # Cycle Structure of Random Permutations with Cycle Weights

Location: MSRI: Simons Auditorium
Speakers: Nicholas Ercolani

Updated on Oct 18, 2010 03:00 AM PDT
694. # PDE's for Gap Probabilities and Applications

Location: MSRI: Simons Auditorium

Updated on Oct 16, 2010 06:08 AM PDT
695. # Reverse-Time Migration and Inverse Scattering, and Applications in Global Seismology

Location: MSRI: Simons Auditorium
Speakers: Maarten de Hoop (Purdue University)

Updated on Sep 05, 2013 12:06 PM PDT
696. # The Kardar-Parisi-Zhang Equation: A Weakly Asymmetric Exclusion Process Approximation.

Location: UC Berkeley
Speakers: Ivan Corwin (Columbia University)

Updated on Oct 17, 2013 06:10 PM PDT
697. # Application of Riemann-Hilbert Problems in Modelling of Cavitating Flow

Location: MSRI: Simons Auditorium
Speakers: Anna Zemlyanova

Pizza Lunch

Updated on Oct 18, 2010 02:57 AM PDT
698. # Berkeley-Stanford Algebraic Geometry Colloquium

Updated on Oct 11, 2010 04:14 AM PDT
699. # Novel Techniques for Acoustic and Electromagnetic Field Manipulations and their Applications

Pizza Lunch

Updated on Oct 18, 2010 02:59 AM PDT
700. # Inverse Problems for Differential Forms on Riemannian Manifolds with Boundary

Location: MSRI: Simons Auditorium
Speakers: Katya Krupchyk

Updated on Oct 16, 2010 05:32 AM PDT
701. # Inverse Problems for Classical and Quantum Random Walks

Location: MSRI: Simons Auditorium

Updated on Oct 11, 2010 03:58 AM PDT
702. # The Beta-Hermite and Beta-Laguerre Processes

Location: MSRI: Simons Auditorium
Speakers: Luen-Chau Li

Updated on Oct 11, 2010 03:25 AM PDT
703. # The Gaussian Free Field in an Interlacing Particle System with Two Different Jump Rates

Location: MSRI: Simons Auditorium
Speakers: Maurice Duits

Updated on Oct 11, 2010 03:27 AM PDT
704. # Designing Coupled Free-Form Surfaces

Location: MSRI: Simons Auditorium
Speakers: Chris Croke

Updated on Oct 11, 2010 03:15 AM PDT
705. # Albrecht Durer, Magic Squares, and Unitary Matrix Integrals

Location: MSRI: Simons Auditorium
Speakers: Jonathan Novak

Pizza Lunch

Updated on Dec 04, 2013 12:45 PM PST
706. # "Closed Circles and Rigidity of Magnetic Flow"

Pizza Lunch

Updated on Oct 11, 2010 03:10 AM PDT
707. # On the Linearized Calderon Problem with Partial Data - A Watermelon Approach

Location: MSRI: Simons Auditorium
Speakers: David Dos Santos Ferreira

Updated on Oct 08, 2010 07:39 AM PDT
708. # Scattering by (Some) Rotating Black Holes

Location: MSRI: Simons Auditorium
Speakers: Semyon Dyatlov

We present several results on scattering by Kerr-de Sitter slowly rotating black hole. In particular, we show that the scattering resolvent is meromorphic in the entire complex plane; its poles are known in astrophysics as quasi-normal modes, and in scattering theory as resonances. We then study the distribution of quasi-normal modes, establishing a resonance free strip and comparing our asymptotic results with the numerics done by physicists. As an application, we prove that linear waves on Kerr-de Sitter metric decay exponentially in a certain compact set.
Updated on May 13, 2013 11:01 PM PDT
709. # Low Temperature Expansion for Matrix Models

Location: MSRI: Simons Auditorium
Speakers: Amir Dembo

Relying on its representation as a solution of certain Schwinger-Dyson equation, we study the low temperature expansion of the limiting spectral measure (and limiting free energy), for random matrix models, in case of potentials which are strictly convex in some neighborhood of each of their finitely many local minima. When applied to suitable polynomial test functions, these expansions are given in terms of the aboslutely convergent generating function of an interesting class of colored maps. This talk is based on a joint work with Alice Guionnet and Edouard Maurel-Segala.
Updated on May 13, 2013 11:01 PM PDT
710. # Representation Theory of the Infinite Symmetric Group and Point Processes of Random Matrix Type

Location: MSRI: Simons Auditorium
Speakers: Eugene Strahov

I am going to discuss determinantal and Pfaffian point processes of random matrix type arising in the the harmonic analysis on the infinite symmetric group. These point processes are defined by probability measures on the Thoma set, and are associated with spherical representations of certain Gelfand pairs. I will review some known results for such determinantal point processes, and will present new explicit formulas for the correlation functions of Pfaffian point processes.
Updated on May 13, 2013 11:01 PM PDT
711. # Radon Phenomenon in PDE and Complex Analysis Problems

Location: MSRI: Simons Auditorium
Speakers: Mark Agranovsky

Radon phenomenon (the terminology is due to L. Ehrenpreis) addresses the situations when one can judge the properties of an object (a function or a manifold) from its restrictions to certain subsets (submanifolds, sections, slices...). In context of PDEs, one wants to know whether a function is a solution of a given PDE if it coincides with solutions of this PDE on a family of submanifolds. In complex analysis, one deals with Cauchy-Riemann equation and is led to a problem of characterization of holomorphic or CR functions or, more generally, holomorphic or CR manifolds, or their boundaries, in terms of zero complex moments on varieties of closed curves. I will present a survey of results of this nature obtained in the last decade for elliptic and Cauchy-Riemann equations. Problems of this type arise, in particular, in integral geometry and tomography.
Updated on May 13, 2013 11:01 PM PDT
712. # Imaging Edges in Random Media

Location: MSRI: Simons Auditorium
Speakers: Fernando Guevara Vasquez

Pizza Lunch

Consider the problem of imaging a reflector (target) from recordings of the echoes resulting from probing the medium with waves emanating from an array of transducers (the array response matrix). We present an algorithm that selectively illuminates the edges or the interior of an extended target by choosing particular subspaces of the array response matrix. For a homogeneous background medium, we characterize these subspaces in terms of the singular functions of a space and wave number restricting operator, which are also called generalized prolate spheroidal wave functions. We discuss results indicating what can be expected from using this algorithm when the medium fluctuates around a constant background medium and the fluctuations can be modeled as a random field.
Updated on May 13, 2013 11:01 PM PDT
713. # Integrable Equations for Random Matrix Spectral Gap Probabilities

Location: MSRI: Simons Auditorium
Speakers: Igor Rumanov

Pizza Lunch

Connections are exposed between integrable equations for spectral gap probabilities of unitary invariant ensembles of random matrices (UE) derived by different --- Tracy-Widom (TW) and Adler-Shiota-van Moerbeke (ASvM) --- methods. Simple universal relations are obtained between these probabilities and their ratios on one side, and variables of the approach using resolvent kernels of Fredholm operators on the other side. A unified description of UE is developed in terms of universal, i.e. independent of the specific probability measure, PDEs for gap probabilities, using the correspondence of TW and ASvM variables. These considerations are based on the three-term recurrence for orthogonal polynomials (OP) and one-dimensional Toda lattice (or Toda-AKNS) integrable hierarchy whose flows are the continuous transformations between different OP bases. Similar connections exist for coupled UE. The gap probabilities for one-matrix Gaussian UE (GUE) or joint gap probabilities for coupled GUE satisfy various PDEs whose number grows with the number of spectral endpoints. With the above connections serving as a guide, minimal complete sets of independent lowest order PDEs for the GUE and for the largest eigenvalues of two-matrix coupled GUE are found.
Updated on May 13, 2013 11:01 PM PDT
714. # Regularized Electrical Impedance Tomography Using Nonlinear Fourier Transform

Location: MSRI: Simons Auditorium
Speakers: Samuli Siltanen

A regularized inversion procedure for is presented two-dimensional electrical impedance tomography. The regularization is based on truncation of the scattering transform; this can be viewed as nonlinear low-pass filtering. This leads to a stable reconstruction of the conductivity; an explicit rate of convergence in appropriate Banach spaces is derived as well. Numerical results are included, demonstrating the convergence of the reconstructed conductivity to the true conductivity as the noise level tends to zero. The results provide a link between two traditions of inverse problems research: theory of regularization and inversion methods based on complex geometrical optics.
Updated on May 13, 2013 11:01 PM PDT
715. # Point Processes in the Complex Plane

Location: MSRI: Simons Auditorium
Speakers: Peter Forrester

I'll discuss my two recent arXiv postings, Non-intersecting Brownian walkers and Yang-Mills theory on the sphere (with Majumdarand Schehr) and The limiting Kac random polynomial and truncated random orthogonal matrices.
Updated on May 13, 2013 11:01 PM PDT
716. # Two Charge Ensembles on the Line.

Location: MSRI: Simons Auditorium
Speakers: Christopher Sinclair

We consider an ensemble of charged particles on the line in the harmonic oscillator potential. Some number of the particles have charge 1 and the remaining have charge 2 and we constrain the ensemble to have a total charge of N. This ensemble is solvable, in that the particles form a Pfaffian point process on the line. A parameter (the fugacity) controls the proportion of particles, and the ensemble interpolates with this parameter between GOE and GSE. I will talk about global results: the density function for the number of each particle, as well as the spatial density of each type of particle for a value of the fugacity which connects this ensemble to Ginibre?s real ensemble. This is joint work with B Rider and Y Xu.
Updated on May 13, 2013 11:01 PM PDT
717. # Gradient Estimate of Solutions of Parabolic Operator with Discontinuous Coefficients.

Location: MSRI: Simons Auditorium
Speakers: Gen Nakamura

An interior gradient estimate of solutions of parabolic operators with discontinuous coefficients and its application to gradient estimates of the fundamental solutions of these operators are given in my talk. The discontinuities of coefficients are across several closed surfaces and some of them can touch each other. The interior estimate is the parabolic version of Li-Vogelius and Li-Nirenberg results. Since the parabolic operators with discontinuous coefficients can model the temperature distribution in heat conductors with inclusions, the result could be useful also for inverse problem such as identifying unknown inclusions which can touch each other. More precisely, what I have in mind is to extend the so-called dynamical probe method which is known as a method to reconstruct the unknown discontinuities of the media, such as cavities and inclusions, to the case that some of the inclusions can touch each other. I will explain how to extract the dominant part of the reflected solution by using the gradient estimate of the fundamental solution. But in order to establish the dynamical probe method for this case, I still need to prove the estimate from below of the modulus of the dominant part of reflected solution.
Updated on May 13, 2013 11:01 PM PDT
718. # The Inverse Calderon Problem for Schrödinger Operator on Riemann Surfaces

Location: MSRI: Simons Auditorium
Speakers: Leo tzou

Pizza Lunch

We show that on a smooth compact Riemann surface with boundary (M0, g) the Dirichletto- Neumann map of the Schrödinger operator â g + V determines uniquely the potential V . This seemingly analytical problem turns out to have connections with ideas in symplectic geometry and differential topology. We will discuss how these geometrical features arise and the techniques we use to treat them. This is joint work with Colin Guillarmou of CNRS Nice. The speaker is partially supported by NSF Grant No. DMS-0807502 during this work.
Updated on May 13, 2013 11:01 PM PDT
719. # E. Nordenstam's Talk

Location: MSRI: Simons Auditorium
Speakers: Eric Nordenstam

Pizza Lunch

Updated on May 13, 2013 11:01 PM PDT
720. # Seismic Imaging with Multiply Scattered Waves

Location: MSRI: Simons Auditorium
Speakers: Alison Malcolm

Most seismic imaging algorithms assume single-scattering, because this linearizes the inverse problem. Multiply-scattered energy can be significant, however, especially if there are strong reflectors in the model. We setup a series expansion that allows for the inclusion of multipy-scattered waves through a sequence of linear problems rather than a single nonlinear problem. This results in an iterative algorithm for imaging with multiply-scattered waves that allows the imaging of structures not illuminated by singly scattered waves by constructing a sequence of images of the subsurface. A downside of this approach is the dependence of subsequent images on previous ones; extensions to mitigate this problem will also be discussed.
Updated on May 13, 2013 11:01 PM PDT
721. # Cloaking: Where Science Fiction Meets Science

Location: UC Berkeley, 60 Evans Hall
Speakers: Graeme Milton

Cloaking involves making an object partly or completely invisible to incoming waves such as sound waves, sea waves or seismic waves, but usually electromagnetic waves such as visible light, microwaves, infrared light, or radio waves. Camouflage and stealth technology achieve partial invisibility, but can one achieve true invisibility from such waves? This lecture will survey some of the wide variety of ideas on cloaking: these include cloaking by plasmonic covers, transformation based cloaking, non Euclidean cloaking, cloaking due to anomalous resonance, cloaking by complementary media, active interior cloaking and active exterior cloaking. Beautiful mathematics is involved.
Updated on May 13, 2013 11:01 PM PDT
722. # When is a Non-self Adjoint Hill Operator of Spectral Type?

Location: MSRI: Simons Auditorium

abstract (.dvi)
Updated on May 13, 2013 11:01 PM PDT
723. # Height Distributions of 1D KPZ Equation with Sharp Wedge Initial Conditions.

Location: MSRI: Simons Auditorium
Speakers: Tomohiro Sasamoto

The Kardar-Parisi-Zhang (KPZ) equation is a nonlinear stochastic differential equation which describes surface growth. We consider the one-dimensional version of the equation with sharp wedge initial conditions. We show that the distributions of the height is written as an integral of a Fredholm determinant. We discuss a few properties of the solution. In the long time limit it tends to the GUE Tracy-Widom distribution. The first order correction is of t^{-1/3} which is consistent with a recent experiment of liquid crystal turbulence. We also explain the derivation of our results based on the contour integral formula for ASEP by Tracy and Widom. This is based on a collaboration with H. Spohn.
Updated on May 13, 2013 11:01 PM PDT
724. # The Two-point Distribution of the One-dimensional Kadar-Parisi-Zhang Equation with Sharp Wedge Initial Data.

Location: MSRI: Simons Auditorium
Speakers: Herbert Spohn

The KPZ equation is a stochastic PDE goverving the motion of a height profile h(x,t). Several groups have obtained the distribution of h(x,t), x,t fixed, and have established that in the long time limit it converges to GUE Tracy Widom. In my talk I will discuss the joint distribution of {h(x_1,t),h(x_2,t)}.
Updated on May 13, 2013 11:01 PM PDT
725. # Collapse to the Orbifolds and Stability of Inverse Problems.

Location: MSRI: Simons Auditorium
Speakers: Yaroslav Kurylev

We consider the IP of the reconstruction of a Riemannian manifold from its spectral data (say heat kernel) on some subset of this manifold. The a priori conditions on the class of manifolds may allow for their one-dimensional collapse giving rise to Riemannian orbifolds. We consider IP on orbifolds and then stability of the IP on the original class of Riemannian manifolds.
Updated on May 13, 2013 11:01 PM PDT
726. # Resistor Networks and Optimal Grids for Electrical Impedance Tomography with Partial Boundary Measurements

Location: MSRI: Baker Board Room
Speakers: Alexander Mamonov

Pizza Lunch

The problem of Electrical Impedance Tomography (EIT) with partial boundary measurements is to determine the electric conductivity inside a body from the simultaneous measurements of direct currents and voltages on a subset of its boundary. Even in the case of full boundary measurements the non-linear inverse problem is known to be exponentially ill-conditioned. Thus, any numerical method of solving the EIT problem must employ some form of regularization. We propose to regularize the problem by using sparse representations of the unknown conductivity on adaptive finite volume grids known as the optimal grids. Then the discretized partial data EIT problem can be reduced to solving the discrete inverse problems for resistor networks. Two distinct approaches implementing this strategy are presented. The first approach uses the results for the EIT problem with full boundary measurements, which rely on the use of resistor networks with circular graph topology. The optimal grids for such networks are essentially one dimensional objects, which can be computed explicitly. We solve the partial data problem by reducing it to the full data case using the theory of extremal quasiconformal (Teichmuller) mappings. The second approach is based on resistor networks with the pyramidal graph topology. Such network topology is better suited for the partial data problem, since it allows for explicit treatment of the inaccessible part of the boundary. We present a method of computing the optimal grids for the networks with general topology (including pyramidal), which is based on the sensitivity analysis of both the continuum and the discrete EIT problems. We present extensive numerical results for the two approaches. We demonstrate both the optimal grids and the reconstructions of smooth and discontinuous conductivities in a variety of domains. The numerical results show two main advantages of our approaches compared to the traditional optimization-based methods. First, the inversion based on resistor networks is orders of magnitude faster than any iterative algorithm. Second, our approaches are able to correctly reconstruct the conductivities of very high contrast, which usually present a challenge to the iterative or linearization-based inversion methods.
Updated on May 13, 2013 11:01 PM PDT
727. # Small Volume Asymptotics and Detection of Defects in Composite Media.

Location: MSRI: Baker Board Room
Speakers: Eric Bonnetier

Numerical methods based on asymptotic expansions have proven quite successful for the detection of small inhomogeneities, embedded in a smooth background medium, using boundary measurements. We consider situations where the size of the inhomogeneities is comparable to the scale of oscillations of the surrounding medium: We assume that the background is a periodic composite medium, or a periodic network, for a conduction equation. In these cases, the asymptotic expansion of the voltage potential is similar to that of a smooth, slowly varying, background. The first order correction term is of dipole type and the material and geometrical properties of the inhomogeneities are expressed through a polarization tensor. We discuss how these expansions may shed light on time reversal experiments in composite media, that showed super-resolution.
Updated on May 13, 2013 11:01 PM PDT
728. # Explicit Approximate Green's Function for Parabolic Equations.

Location: MSRI: Baker Board Room
Speakers: Anna Mazzucato

We construct explicitly computable approximations to the Green's function of certain second-order parabolic equations, using Dyson series, Taylor expansions and exact commutator formulas. These approximations are accurate to arbitrary order in the short-time limit, and can be extended to large time by combining with numerical bootstrapping. The method applies also to certain kinds of degenerate equations, such as Fokker-Planck equations arising in pricing of contingent claims. A main motivation for this work is parameter estimation via Bayesian inference.
Updated on May 13, 2013 11:01 PM PDT
729. # EIT in 2D: The Issue of Stability.

Location: MSRI: Baker Board Room
Speakers: Alberto Ruiz Gonzalez

We will show that under some control of oscillation (measured in Sobolev norm) one can prove logarithmic stability in the Inverse problem of Calderon. The results is a joint work with A. Clop and D. Faraco and includes conductivities not necesarely continuous.
Updated on May 13, 2013 11:01 PM PDT
730. # Beyond the Gaussian Universality Class

Location: UC Berkeley, 60 Evans Hall
Speakers: Ivan Corwin

Refreshments following the lecture at La Val's Pizza, 1834 Euclid Ave. sponsored by MSRI

The Gaussian central limit theorem says that for a wide class of stochastic systems, the bell curve (Gaussian distribution) describes the statistics for random fluctuations of important observables. In this talk I will look beyond this class of systems to a collection of probabilistic models which include random growth models, polymers, particle systems, PDEs and matrices, as well as certain asymptotic problems in combinatorics and representation theory. I will explain in what ways these different examples all fall into a single new universality class with a much richer mathematical structure than that of the Gaussian. The full scope and structure of this new universality class is just one of many important open questions being studied at MSRI this fall.
Updated on May 13, 2013 11:01 PM PDT
731. # The Interior Transmission Eigenvalue Problem for Maxwell's Equations

Location: MSRI: Baker Board Room
Speakers: Andreas Kirsch

After a short introduction into the scattering theory for electromagnetic time harmonic plane waves by an inhomogeneous medium with (possibly anisotropic) dielectricity I will adress the question under which assumptions the corresponding far field operator is injective. This leads to an unusual non self adjoint eigenvalue problem. I will show how to prove discreteness of the spectrum and existence of real eigenvalues.
Updated on May 13, 2013 11:01 PM PDT
732. # Incoming and Disappearing Solutions for Maxwell's equations

Location: MSRI: Simons Auditorium
Speakers: Vesselin Petkov

We prove that in contrast to the free wave equation in $\R3$ there are no incoming solutions of Maxwell's equations in the form of spherical or modulated spherical waves. We construct solutions which are corrected by lower order incoming waves. With their aid, we construct dissipative boundary conditions and solutions to Maxwell's equations in the exterior of a sphere which decay exponentially as $t \to + \infty$. They are asymptotically disappearing. Disappearing solutions which are identically zero for $t \geq T > 0$ are constructed which satisfy maximal dissipative boundary conditions which depend on time $t.$ Both types of solutions are invisible in scattering theory and the existence of such solutions perturbs the inverse scattering.
Updated on May 13, 2013 11:01 PM PDT
733. # Random Matrices Beyond the Usual Universality Classes

Location: MSRI: Simons Auditorium
Speakers: Ken McLaughlin

The statistical behavior of eigenvalues of large random matrices (i.e. in the limit when the matrix size tends to infinity) has been thoroughly investigated, for probability densities of the form C \exp{ - Tr V ( M ) } where V(x) is a smooth, real valued function of the real variable x, and V(M) is defined on matrices by "the usual procedure". First goal: provide a background and introduction to the above. But for probability densities in which the TRACE does not appear linearly, the situation is less understood. A simple example is: C \exp{ ( Tr ( M2 ) )2 } (i.e. square the trace). Second goal: explain the source of the complication. Third goal: Describe results. (Joint work with Misha Stepanov, Univ. of Arizona)
Updated on May 13, 2013 11:01 PM PDT
734. # Exact Solution of the Antiferroelectric Six-vertex Model. Riemann-Hilbert Approach.

Location: MSRI: Simons Auditorium
Speakers: Pavel Bleher

Updated on May 13, 2013 11:01 PM PDT
735. # Reconstruction of Small Elastic Inclusions from Boundary Measurements

Location: MSRI: Baker Board Room
Speakers: Elena Beretta

We first derive a rigorous asymptotic formula for the perturbation of the displacement field in an isotropic elastic material in the presence of thin isotropic inhomogeneities. We then use this formula for the reconstruction of the inclusions from boundary measurements.
Updated on May 13, 2013 11:01 PM PDT
736. # Random Matrix Theory-Informal Seminar

Location: MSRI: Baker Board Room

Updated on May 13, 2013 11:01 PM PDT
737. # Fall 2010- 5-minute Presentations

Location: MSRI: Simons Auditorium

PIZZA LUNCH

10:00 – 10:05 10:06 – 10:11 Fernando Guevara Vasquez 10:12 – 10:17 Vladislav Kargin 10:18 – 10:23 Leo Tzou 10:24 – 10:29 Benjamin Young 10:30 – 10:35 Pilar Herreros 10:36 – 10:41 Jonathan Novak 10:42 – 10:47 Juha-Matti Perkkio 10:48 – 10:53 Eric Nordenstam 10:54 – 10:59 Hamid Hezari 11:00 – 11:15 Break 11:15 – 11:20 Anna Zemlyanova 11:21 – 11:26 Linh Nguyen 11:27 – 11:32 Igor Rumanov 11:33 – 11:38 Alexander Mamonov 11:39 – 11:44 Martin Bender 11:45 – 11:50 Kiril Datchev 11:51 – 11:56 Alison Malcolm 12:00-2:00 Pizza Lunch 2:00-2:05 Jacob White 2:06-2:11 Chris Croke 2:12 – 2:17 Brigitte Servatius 2:18 – 2:23 Leonid Pestov 2:24 – 2:29 Samuli Siltanen 2:30 – 2:35 Matti Lassas
Updated on May 13, 2013 11:01 PM PDT
738. # Photoacoustic Tomography: Breaking through the Optical Diffusion Limit

Location: UC Berkeley, 60 Evans Hall
Speakers: Lihong Wang

There will be refreshments following the lecture at La Val's Pizza, 1834 Euclid Avenue, sponsored by MSRI.

We develop photoacoustic imaging technologies for in vivo early-cancer detection and functional or molecular imaging by physically combining non-ionizing electromagnetic and ultrasonic waves. Unlike ionizing x-ray radiation, non-ionizing electromagnetic waves—such as optical and radio waves—pose no health hazard and reveal new contrast mechanisms. Unfortunately, electromagnetic waves in the non-ionizing spectral region do not penetrate biological tissue in straight paths as x-rays do. Consequently, high-resolution tomography based on non-ionizing electromagnetic waves alone—such as confocal microscopy, two-photon microscopy, and optical coherence tomography—is limited to superficial imaging within approximately one optical transport mean free path (~1 mm in the skin) of the surface of scattering biological tissue. Ultrasonic imaging, on the contrary, provides good image resolution but has strong speckle artifacts as well as poor contrast in early-stage tumors. Ultrasound-mediated imaging modalities that combine electromagnetic and ultrasonic waves can synergistically overcome the above limitations. The hybrid modalities provide relatively deep penetration at high ultrasonic resolution and yield speckle-free images with high electromagnetic contrast. In photoacoustic computed tomography, a pulsed broad laser beam illuminates the biological tissue to generate a small but rapid temperature rise, which leads to emission of ultrasonic waves due to thermoelastic expansion. The short-wavelength pulsed ultrasonic waves are then detected by unfocused ultrasonic transducers. High-resolution tomographic images of optical contrast are then formed through image reconstruction. Endogenous optical contrast can be used to quantify the concentration of total hemoglobin, the oxygen saturation of hemoglobin, and the concentration of melanin. Melanoma and other tumors have been imaged in vivo. Exogenous optical contrast can be used to provide molecular imaging and reporter gene imaging. In photoacoustic microscopy, a pulsed laser beam is focused into the biological tissue to generate ultrasonic waves, which are then detected with a focused ultrasonic transducer to form a depth resolved 1D image. Raster scanning yields 3D high-resolution tomographic images. Super-depths beyond the optical diffusion limit have been reached with high spatial resolution. Thermoacoustic tomography is similar to photoacoustic tomography except that low-energy microwave pulses, instead of laser pulses, are used. Although long-wavelength microwaves diffract rapidly, the short-wavelength microwave-induced ultrasonic waves provide high spatial resolution, which breaks through the microwave diffraction limit. Microwave contrast measures the concentrations of water and ions. The annual conference on this topic has been doubling in size approximately every three years since 2003 and has become the largest in SPIE’s Photonics West as of 2009.
Updated on May 13, 2013 11:01 PM PDT
739. # Legendrian tangles and box-dot diagrams for "regular" rational tangles

Location: MSRI: Simons Auditorium
Speakers: Greg Schneider

We introduce a new presentation for rational tangles which to the number theory of positive regular continued fractions. This presentation also admits a suitable extension to the contact setting, allowing us to define a natural Legendrian embedding of a particular class of rational tangles into the standard contact Euclidean 3-space. We will briefly discuss how these box-dot diagrams, along with an associated construction, can be used to determine when the Legendrian flyping operation yields tangles which are not Legendrian isotopic, further refining an earlier result of Traynor.
Updated on May 13, 2013 11:01 PM PDT
740. # Postdoctoral Seminar

Location: MSRI: Simons Auditorium

Roman Golovko and Jeremy Van Horn-Morris
Updated on May 13, 2013 11:01 PM PDT
741. # Postdoctoral Seminar

Location: MSRI: Simons Auditorium

Roman Golovko (Symplectic and Contact Geometry and Topology)
Updated on May 13, 2013 11:01 PM PDT
742. # Research Seminar: "Constructing braid group actions"

Location: MSRI: Simons Auditorium
Speakers: Sabin Cautis

Abstract: I'll discuss a general approach for constructing braid group actions (and subsequently knot homologies). This can be used to define knot homologies via algebro-geometric methods but I don't know yet of any applications in symplectic geometry (although mirror symmetry suggests there ought to be).
Updated on May 13, 2013 11:01 PM PDT
743. # Quantitative symplectic geometry seminar: "The virtual moduli cycle revisited"

Location: MSRI: Simons Auditorium
Speakers: Dusa McDuff

Updated on May 13, 2013 11:01 PM PDT
744. # Learning seminar: "Coisotropic intersections"

Location: MSRI: Baker Board Room
Speakers: Viktor Ginzburg

Updated on May 13, 2013 11:01 PM PDT
745. # Research Seminar: "Hyperkaehler Floer theory as an infinite dimensional Hamiltonian system on the loop space"

Location: MSRI: Simons Auditorium
Speakers: Sonja Hohloch

Updated on May 13, 2013 11:01 PM PDT
746. # Morse theory on manifolds with boundary

Location: MSRI: Simons Auditorium
Speakers: Petya Pushkar

Updated on May 13, 2013 11:01 PM PDT
747. # Indefinite Morse 2-functions

Location: MSRI: Simons Auditorium
Speakers: David Gay

Updated on May 13, 2013 11:01 PM PDT
748. # MSRI Evans Lecture Series: Symplectic embeddings and continued fractions

Location: UC Berkeley, 60 Evans Hall
Speakers: Dusa McDuff

As shown by Gromov's nonsqueezing theorem, symplectic embedding problems lie at the heart of symplectic topology. The four dimensional problem is rather different from that in higher dimensions. Recently it has become possible to specify exactly when a four dimensional ellipsoid embeds in a ball. The talk explains recent joint work with Schlenk on this question, exploring its unexpected connections to continued fractions, Fibonacci numbers and lattice packing problems.
Updated on May 13, 2013 11:01 PM PDT
749. # Postdoctoral Seminar

Location: MSRI: Simons Auditorium

Sikimeti Ma'u (Symplectic and Contact Geometry and Topology) Cagatay Kutluhan (Homology Theories of Knots and Links)
Updated on May 13, 2013 11:01 PM PDT
750. # Bordered Floer homology working group

Location: MSRI: Baker Board Room
Speakers: Dylan Thurston

Updated on May 13, 2013 11:01 PM PDT
751. # Research Seminar: "Transverse knot invariants via contact surgery"

Location: MSRI: Simons Auditorium
Speakers: Paolo Lisca

I will define new transverse knot invariants using contact surgery, and I will describe some of their properties using the contact Ozsvath-Szabo invariant. This is joint work with Andras Stipsicz.
Updated on May 13, 2013 11:01 PM PDT
752. # Department of Mathematics, University of California 2010 Chern Lectures: "Lecture 4: Heegaard Floer homology and surgery formulas"

Location: UC Berkeley, 60 Evans Hall
Speakers: Peter Ozsváth

After setting up some necessary background, I will turn attention to surgery formulas for reconstructing the Heegaard Floer homology groups of three-manifolds obtained as surgeries on knots and links. I will then explain how this can be used to, in principle, compute Heegaard Floer homology groups of closed (three- and four-) manifolds from data associated to grid diagrams.
Updated on May 13, 2013 11:01 PM PDT
753. # Quantitative symplectic geometry seminar: "Maslov class rigidity for coisotropic manifolds"

Location: MSRI: Simons Auditorium
Speakers: Viktor Ginzburg

Updated on May 13, 2013 11:01 PM PDT
754. # Learning seminar: "Rational and Ruled symplectic 4-manifolds"

Location: MSRI: Baker Board Room
Speakers: Dusa McDuff

Updated on May 13, 2013 11:01 PM PDT
755. # Department of Mathematics, University of California 2010 Chern Lectures: "Lecture 3: Bordered Floer homology"

Location: UC Berkeley, Sibley Auditorium, Bechtel Hall
Speakers: Peter Ozsváth

I will describe an extension of the U=0 specialization of Heegaard Floer homology, HF, to three-manifolds with parameterized boundary. The resulting theory, bordered Floer homology, associates a differential algebra to an oriented two-manifold, and a differential module module over that algebra to a three-manifold with boundary. These differential modules can also be used to reconstruct HF for closed three-manifolds. This is joint work with Robert Lipshitz and Dylan Thurston.
Updated on May 13, 2013 11:01 PM PDT
756. # Research Seminar: "Quantum classes, Mumford conjecture and Hofer geometry"

Location: MSRI: Simons Auditorium
Speakers: Yakov Savelyev

Updated on May 13, 2013 11:01 PM PDT
757. # Postdoctoral Seminar

Location: MSRI: Simons Auditorium

Yanki Lekili (Symplectic and Contact Geometry and Topology) Andrew Lobb (Homology Theories of Knots and Links)
Updated on May 13, 2013 11:01 PM PDT
758. # Bordered Floer homology working group: Group discussion.

Location: MSRI: Baker Board Room

Updated on May 13, 2013 11:01 PM PDT
759. # Research Seminar: "J-holomorphic curves for the ECH = Heegard/Floer correspondence"

Location: MSRI: Simons Auditorium
Speakers: Clifford Taubes

I plan to describe the J-holomorphic curves that enter when computing the Heegard-Floer homology for a genus g Heegard splitting of a given 3-manifold using the embedded contact homology for a certain contact 1-form on the connect sum of the original manifold with g+1 copies of S1 x S2
Updated on May 13, 2013 11:01 PM PDT
760. # Department of Mathematics, University of California 2010 Chern Lectures: "Lecture 2: Knot Floer homology"

Location: UC Berkeley, Sibley Auditorium, Bechtel Hall
Speakers: Peter Ozsváth

Heegaard Floer homology can be used to define an invariant for knots in the three-sphere. This invariant, whose definition involves holomorphic curves, admits an elementary, combinatorial description in terms of grid diagrams. I will describe the construction, and sketch a combinatorial proof of its topological invariance. This lecture will cover joint work with Ciprian Manolescu, Sucharit Sarkar, Zoltán Szabó, and Dylan Thurston.
Updated on May 13, 2013 11:01 PM PDT
761. # Quantitative Floer theory working group: " Uniqueness of generating Hamiltonians for continuous Hamiltonian flows"

Location: MSRI: Simons Auditorium
Speakers: Lev Buhovski

Updated on May 13, 2013 11:01 PM PDT
762. # Learning Seminar: " An introduction to contact homology for Legendrian knots"

Location: MSRI: Baker Board Room
Speakers: Lenhard Ng

Updated on May 13, 2013 11:01 PM PDT
763. # Department of Mathematics, University of California 2010 Chern Lectures: "Lecture 1: Introduction to Heegaard Floer homology"

Location: UC Berkeley, Sibley Auditorium, Bechtel Hall
Speakers: Peter Ozsvath

Heegaard Floer homology is an invariant for low-dimensional manifolds defined using methods from symplectic geometry (holomorphic disks, Lagrangian Floer homology). To a closed, oriented three-manifold, this invariant associates a module over the polynomial algebra in a formal variable U. I will outline the structure of this theory and discuss various of its topological applications. This construction (as an invariant for three- and four-manifolds) was originally discovered in collaboration with Zoltán Szabó. The generalization to knots was discovered independently by Jacob Rasmussen.
Updated on May 13, 2013 11:01 PM PDT
764. # Research Seminar: "Indefinite Morse 2-functions"

Location: MSRI: Simons Auditorium
Speakers: David Gay

This is joint work with Rob Kirby, inspired and motivated by work of Tim Perutz and Yanki Lekili on the possibility of extracting smooth 4-manifold invariants from broken Lefschetz fibrations over the sphere. A "Morse 2-function" is a suitably generic smooth map from an n-manifold to a 2-manifold, just as a Morse function is a suitably generic map to a 1-manifold. Locally, Morse 2-functions look like $(t,p) \mapsto (t,g_t(p))$, where $g_t$ is a generic homotopy between Morse functions (on an (n-1)--manifold), so thinking about Morse 2-functions is something like thinking about Cerf theory when you can't say globally what direction should be called "time". An indefinite Morse 2-function is one in which, in this local model, the Morse function $g_t$ never has critical points of minimal or maximal index. We prove existence and uniqueness results for indefinite Morse 2-functions over the disk and the sphere. "Uniqueness" means that homotopic indefinite Morse 2-functions can be connected by generic homotopies which are indefinite at all intermediate times. Some of our results have already been proved by Saeki and Williams, but we have a number of important improvements, most notably that we can keep fibers connected at all times and that the results for the sphere follow as corollaries from the results for the disk. We also think that the perspective on Morse 2-functions which comes from our methods of proof is enlightening in and of itself and worth sharing.
Updated on May 13, 2013 11:01 PM PDT
765. # MSRI Evans Lecture Series: "Exotic smooth 4-manifolds"

Location: UC Berkeley, 60 Evans Hall
Speakers: András Stipsicz

4-dimensional manifolds exhibit phenomena which do not happen in any other dimension: there are examples of infinitely many smooth 4-manifolds which are homeomorphic but not diffeomorphic. The ’exotic’ behaviour of a smooth 4-manifold seems to be very closely related to the genera of 2-dimensional surfaces it contains. We will discuss a method for changing the differentiable structure of the famous K3-surface.
Updated on May 13, 2013 11:01 PM PDT
766. # Postdoctoral Seminar

Location: MSRI: Simons Auditorium

Sonja Hohloch (Symplectic and Contact Geometry and Topology) Radmila Sazdanovic (Homology Theories of Knots and Links)
Updated on May 13, 2013 11:01 PM PDT
767. # Bordered Floer homology working group

Location: MSRI: Baker Board Room
Speakers: Rumen Zarev

Updated on May 13, 2013 11:01 PM PDT
768. # Research Seminar: "Twisted Alexander polynomials and the Thurston norm"

Location: MSRI: Simons Auditorium
Speakers: Stefan Friedl

Given a knot K and a representation one can define the twisted Alexander polynomials of the knot K. Degrees of twisted Alexander polynomials give in particular lower bounds on the Seifert genus. Using recent results of Agol and Wise we will show that twisted Alexander polynomials detect the genus of hyperbolic knots. This result has an application to the problem of determing the minimal complexity of surfaces in 4-manifolds which are S^1-bundles over a 3-manifold.
Updated on May 13, 2013 11:01 PM PDT
769. # Quantitative Floer theory working group: " Invariants of smooth embeddings via contact geometry"

Location: MSRI: Simons Auditorium
Speakers: John Etnyre

Updated on May 13, 2013 11:01 PM PDT
770. # Learning seminar: "The moment map and equivariant cohomology theories"

Location: MSRI: Baker Board Room
Speakers: Tara Holm

Updated on May 13, 2013 11:01 PM PDT
771. # Research Seminar: "Wild symplectic structures, mean curvature flow and holomorphic discs"

Location: MSRI: Simons Auditorium
Speakers: Brendan Guilfoyle

Updated on May 13, 2013 11:01 PM PDT
772. # Postdoctoral Seminar

Location: MSRI: Simons Auditorium

Maksim Maydanskiy (Symplectic and Contact Geometry and Topology) Helge Ruddat (Homology Theories of Knots and Links)
Updated on May 13, 2013 11:01 PM PDT
773. # Bordered Floer homology working group

Location: MSRI: Baker Board Room
Speakers: Jen Hom

Updated on May 13, 2013 11:01 PM PDT
774. # Research Seminar: "Heegaard Floer homology and integer surgeries on links"

Location: MSRI: Simons Auditorium
Speakers: Ciprian Manolescu

Updated on May 13, 2013 11:01 PM PDT
775. # Sutured Contact Homology

Location: MSRI: Simons Auditorium
Speakers: Paolo Ghiggini

Updated on May 13, 2013 11:01 PM PDT
776. # Quantitative Floer theory working group: "Cyclic symmetry, enumerative invariants and mirror symmetry"

Location: MSRI: Simons Auditorium
Speakers: Kenji Fukaya

Updated on May 13, 2013 11:01 PM PDT
777. # Learning seminar: "Introduction to contact invariants in Heegaard-Floer theory"

Location: MSRI: Baker Board Room
Speakers: Vera Vertesi

Updated on May 13, 2013 11:01 PM PDT
778. # Research Seminar: The growth rate of symplectic homology and applications

Location: MSRI: Simons Auditorium
Speakers: Mark McLean

Updated on May 13, 2013 11:01 PM PDT
779. # MSRI Evans Lecture Series: "Slicing and surgery"

Location: UC Berkeley, 60 Evans Hall
Speakers: Jacob Rasmussen

I'll introduce two classical problems in low dimensional topology: finding rational knots which are slice and finding knots in the solid torus with solid tours surgeries. Then I'll explain why these two problems are actually one and the same.
Updated on May 13, 2013 11:01 PM PDT
780. # Postdoctoral Seminar

Location: MSRI: Simons Auditorium

Visiting Postdocs: Gregor Noetzel, Andrew Cotton-Clay
Updated on May 13, 2013 11:01 PM PDT
781. # Bordered Floer homology working group.

Location: MSRI: Baker Board Room
Speakers: Tova Brown

Updated on May 13, 2013 11:01 PM PDT
782. # Research Seminar: "Grid Diagrams and Schubert varieties"

Location: MSRI: Simons Auditorium
Speakers: Christian Kassel

Recently, Manulescu, Ozsváth, Sarkar, Szábo, D. Thurston gave a combinatorial construction of the Heegaard-Floer homology of links based on the presentation of links by "grid diagrams." I will show how grid diagrams can be used to solve a problem in a different area, namely the determination of the singular locus of a Schubert variety. My talk is based on joint work with Alain Lascoux and Christophe Reutenauer (J. of Algebra, 2003).
Updated on May 13, 2013 11:01 PM PDT
783. # Working Group "Quantitative Floer theory" Symplectic embedding obstructions from ECH

Location: MSRI: Simons Auditorium
Speakers: Michael Hutchings

Updated on May 13, 2013 11:01 PM PDT
784. # Learning seminar: "An introduction to Lefschetz fibrations"

Location: MSRI: Baker Board Room
Speakers: Denis Auroux

Updated on May 13, 2013 11:01 PM PDT
785. # Research Seminar: " Lagrangian caps for Legendrian knots via Generating families"

Location: MSRI: Simons Auditorium
Speakers: Joshua Sabloff

Updated on May 13, 2013 11:01 PM PDT
786. # MSRI Evans Lecture Series: "What we know and don't know about 4-dimensions"

Location: UC Berkeley, 60 Evans Hall
Speakers: Clifford Taubes

This talk is for those who know nothing about 4 dimensional spaces, but hope to learn where the boundary lies between ignorance and knowledge. As I hope to explain, the boundary is quite sharp and easy to see.
Updated on May 13, 2013 11:01 PM PDT
787. # Postdoctoral Seminar

Location: MSRI: Simons Auditorium

John Baldwin (Symplectic and Contact Geometry and Topology) Yasuyoshi Yonezawa (Homology Theories of Knots and Links)
Updated on May 13, 2013 11:01 PM PDT
788. # Bordered Floer homology working group

Location: MSRI: Baker Board Room

Updated on May 13, 2013 11:01 PM PDT
789. # Symplectic Topology today

Location: MSRI: Simons Auditorium
Speakers: Dusa McDuff

Updated on May 13, 2013 11:01 PM PDT
790. # From Whitney disks to the Jacobi identity

Location: MSRI: Simons Auditorium
Speakers: Peter Teichner

Updated on May 13, 2013 11:01 PM PDT
791. # On Knot Homology Theories

Location: MSRI: Simons Auditorium
Speakers: Eli Grigsby

Updated on May 13, 2013 11:01 PM PDT
792. # Transverse knots and Heegaard Floer homology

Location: MSRI: Simons Auditorium
Speakers: Lenhard Ng

Updated on May 13, 2013 11:01 PM PDT
793. # "K12 Math Teacher Preparation: What Math Departments Can Do"

Location: MSRI: Simons Auditorium

Updated on May 13, 2013 11:01 PM PDT
794. # Bordered Floer: from 2 to 4

Location: MSRI: Simons Auditorium
Speakers: Robert Lipshitz

Bordered Floer theory is an extension of Heegaard Floer homology to surfaces and 3-manifold with boundary. After surveying the general structure of bordered Floer homology, we will see how it can be used to compute various classical parts of the Heegaard Floer package: the closed three manifold invariant HF-hat, the cobordism maps on HF-hat, and the link surgery spectral sequence. These computations follow almost entirely from formal properties of the theory. This is joint work with Peter Ozsvath and Dylan Thurston.
Updated on May 13, 2013 11:01 PM PDT
795. # Working Group "Quantitative Floer theory"

Location: MSRI: Simons Auditorium
Speakers: Basak Gurel

Updated on May 13, 2013 11:01 PM PDT
796. # HTKL Graduate Student Seminar

Location: MSRI: Simons Auditorium

Updated on May 13, 2013 11:01 PM PDT
797. # Learning seminar: "An introduction to quasi-states and quasi-morphisms" (and recent work of Entov-Polterovich)

Location: MSRI: Baker Board Room
Speakers: Leonid Polterovich

Updated on May 13, 2013 11:01 PM PDT
798. # Research Seminar: "Quadrics, instantons, and representation varieties"

Location: MSRI: Simons Auditorium
Speakers: Ivan Smith

Updated on May 13, 2013 11:01 PM PDT
799. # Postdoctoral Seminar

Location: MSRI: Simons Auditorium

Vera Vertesi (Symplectic and Contact Geometry and Topology) Sucharit Sarkar (Homology Theories of Knots and Links)
Updated on May 13, 2013 11:01 PM PDT
800. # Bordered Floer homology working group.

Location: MSRI: Baker Board Room
Speakers: Yi Ni

Updated on May 13, 2013 11:01 PM PDT
801. # Working Group "Quantitative Floer theory"

Location: MSRI: Simons Auditorium

Updated on May 13, 2013 11:01 PM PDT
802. # Working Group "Symplectic geometry and representation theory" Topic: Mirror symmetry for the cotangent bundle of the $2$-sphere

Location: MSRI: Simons Auditorium
Speakers: Denis Auroux

Updated on May 13, 2013 11:01 PM PDT
803. # Learning seminar: "A basic introduction to open book decompositions and invariants of contact structures"

Location: MSRI: Baker Board Room
Speakers: John Etnyre

Updated on May 13, 2013 11:01 PM PDT
804. # Research Seminar: "Link invariants and the structure of Fukaya categories"

Location: MSRI: Simons Auditorium

Updated on May 13, 2013 11:01 PM PDT
805. # MSRI Evans Lecture Series: "How to detect unknottedness using instantons and Khovanov homology"

Location: UC Berkeley, 60 Evans Hall
Speakers: Tomasz Mrowka

There are now many, many invariants of knots and links coming from many sources, algebraic topology, representation theory, statistical mechanics, gauge theory and symplectic geometry. A basic question about these invariants is whether they can detect the unknot. Some classical invariants, like the Alexander polynomial cannot, while others like the knot group can. More modern invariants like the various Floer homology theory based on Instantons, Seiberg-Witten monopoles or Ozvath and Szabo's Heegaard Floer homology all can detect the unknot. The status of the Jones polynomial remains undetermined. I will try to explain why some of these theories are able to detect the unknot and mention some recent work of Kronheimer and myself that leads to a proof that Khovanov homology detects the unknot by relating Khovanov homology to a version of Instanton Floer homology.
Updated on May 13, 2013 11:01 PM PDT
806. # Postdoctoral Seminar

Location: MSRI: Simons Auditorium

Joel Fish (Symplectic and Contact Geometry and Topology) Josh Greene (Homology Theories of Knots and Links)
Updated on May 13, 2013 11:01 PM PDT
807. # Khovanov homology is an unknot detector II

Location: MSRI: Simons Auditorium
Speakers: Tomasz Mrowka

This will be a series of lectures over the course of the program outlining the proof of Kronheimer and myself that Khovanov homology detects the unknot. The main tool that is used is a version of Floer homology which uses connections with prescribed singularities along the knot. This first two talks will explain in some detail the construction of instanton Floer homology and its generalization to connections with singularities. I will try to build things up from scratch as much as possible so the talks should be accessible to graduate students.
Updated on May 13, 2013 11:01 PM PDT
808. # Working Group "Quantitative Floer theory": Symplectic rigidity of Lagrangian cylinders

Location: MSRI: Simons Auditorium
Speakers: Joshua Sabloff

Updated on May 13, 2013 11:01 PM PDT
809. # Working Group "Symplectic geometry and representation theory"

Location: MSRI: Simons Auditorium
Speakers: Catharina Stroppel

Updated on May 13, 2013 11:01 PM PDT
810. # Learning seminar: "An introduction to symplectic Khovanov homology"

Location: MSRI: Baker Board Room

Updated on May 13, 2013 11:01 PM PDT
811. # Khovanov homology is an unknot detector I

Location: MSRI: Simons Auditorium
Speakers: Tomasz Mrowka

This will be a series of lectures over the course of the program outlining the proof of Kronheimer and myself that Khovanov homology detects the unknot. The main tool that is used is a version of Floer homology which uses connections with prescribed singularities along the knot. This first two talks will explain in some detail the construction of instanton Floer homology and its generalization to connections with singularities. I will try to build things up from scratch as much as possible so the talks should be accessible to graduate students.
Updated on May 13, 2013 11:01 PM PDT
812. # Research Seminar: "Flexibility versus rigidity for tight confoliations"

Location: MSRI: Simons Auditorium
Speakers: Thomas Vogel

Updated on May 13, 2013 11:01 PM PDT
813. # Knot homologies and slice genus bounds

Location: MSRI: Simons Auditorium
Speakers: Andrew Lobb

We will discuss the history of lower bounds on the slice (or "4-ball") genus of a knot, some bounds coming from knot homologies, and the relationship of the history to the knot homological bounds.
Updated on May 13, 2013 11:01 PM PDT
814. # Working Group "Symplectic geometry and representation theory"

Location: MSRI: Simons Auditorium
Speakers: Mohammed Abouzaid

The Fukaya category for the simplest non-cotangent bundle, and Sabin Cautis, Noncommutative quiver varieties
Updated on May 13, 2013 11:01 PM PDT
815. # Working Group: "Quantitative Floer theory"

Location: MSRI: Simons Auditorium
Speakers: Dusa McDuff

Updated on May 13, 2013 11:01 PM PDT
816. # Learning seminar: "An introduction to embedded contact homology"

Location: MSRI: Baker Board Room
Speakers: Michael Hutchings

Updated on May 13, 2013 11:01 PM PDT
817. # Research Seminar "The chord conjecture in three dimensions"

Location: MSRI: Simons Auditorium
Speakers: Michael Hutchings

Updated on May 13, 2013 11:01 PM PDT
818. # MSRI Evans Lecture Series: "Constructing open symplectic manifolds via Lefschetz fibration"

Location: UC Berkeley, 60 Evans Hall
Speakers: Paul Seidel

Lefschetz fibrations give a simple way of constructing a lot of examples of open symplectic manifolds. There are some surprises along the way, and also issues which are still poorly understood.
Updated on May 13, 2013 11:01 PM PDT
819. # Postdoctoral Seminar

Location: MSRI: Simons Auditorium

Mark McLean (SCGT) and Liam Watson (HTKL)
Updated on May 13, 2013 11:01 PM PDT
820. # Zero-crossing and one-crossing knots in thickened surfaces

Location: MSRI: Simons Auditorium
Speakers: Yi Ni

Let $K$ be a knot in a thickened surface $F\times I$. Suppose a nontrivial surgery on $K$ yields a manifold which is homeomorphic to $F\times I$, then the minimal projection of $K$ on $F$ has either zero or one crossing. I will discuss the proof, as well as some further questions in gauge theory and Floer homology.
Updated on May 13, 2013 11:01 PM PDT
821. # Quantitative Floer theory working group: "Some Measurements in Floer theory"

Location: MSRI: Simons Auditorium
Speakers: Leonid Polterovich

Updated on May 13, 2013 11:01 PM PDT
822. # Working Group "Symplectic geometry and representation theory"

Location: MSRI: Simons Auditorium

Updated on May 13, 2013 11:01 PM PDT
823. # Informal organizational meeting for a graduate student learning seminar in symplectic and contact geometry.

Location: MSRI: Baker Board Room