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  1. Postdoc Seminar I: What is a simple closed curve in a free group?: Curve graph analogues for free group automorphisms.

    Location: MSRI: Simons Auditorium
    Speakers: Richard Wade (University of British Columbia)

    The curve complex (or graph if we are only interested in its 1-skeleton) is a wonderful tool for proving theorems about mapping class groups of surfaces. Some of these theorems are also true, or we at least hope are true, for automorphism groups of free groups. Much recent progress has focused on understanding analogous objects to the curve graph in the free group setting. We will give a survey of some recent results. We talk about one reason for the existence of multiple graphs in this setting: there is more than one way of describing what a ‘simple closed curve in a surface’ should be in a free group.

    Updated on Sep 02, 2016 02:10 PM PDT
  2. Postdoc Seminar II: An invitation from non-discrete groups

    Location: MSRI: Simons Auditorium
    Speakers: David Hume (Université de Paris XI)
    I will present a colloquium-style talk aimed at introducing some classical and more recent developments in the theory of totally disconnected locally compact groups. The goal is to highlight the similarities and differences between the current theory of tdlc groups and the more familiar theory of countable and finitely generated groups, and to inspire more people to take an interest in this rapidly developing genre of geometric group theory.
    Updated on Aug 26, 2016 09:35 AM PDT
  3. Postdoc Seminar I: Dimensions of Discrete Groups

    Location: MSRI: Simons Auditorium
    Speakers: Robert Kropholler (University of Oxford)
    I will compare the notions of geometric, CAT(0), CAT(-1) and cubical dimension for discrete groups. I will give examples of groups where these are different and discuss some ideas for future work.
    Updated on Aug 26, 2016 09:19 AM PDT
  4. Postdoc Lunch Seminar II: Unnormalized conical Kahler-Ricci flow

    Location: MSRI: Simons Auditorium
    Speakers: Liangming Shen (University of British Columbia)

    Given a conic metric along a simple normal crossing divisor, we consider the conical Kahler-Ricci flow which preserves the conic structure. We use approximation method to construct the solutions on the largest time interval. Then we establish high order estimates for such flow solution. Finally we briefly introduce some convergence results.

    Updated on Apr 21, 2016 03:27 PM PDT
  5. Postdoc Lunch Seminar I: Special Hermitian metrics characterized by relationships between scalar curvatures

    Location: MSRI: Simons Auditorium
    Speakers: Michael Lock (University of Texas)

    On a Kahler manifold there is a clear connection between the  complex geometry and underlying Riemannian geometry, which can be used to characterize the Kahler condition. While such a link is not as clear in the non-Kahler setting, one can seek to understand these  characterizations as specific instances of a more general type.  I will address such questions from the perspective  of relationships between the Chern and Riemannian scalar curvatures. This is joint work with Michael Dabkowski.

    Updated on Apr 21, 2016 03:26 PM PDT
  6. Postdoc Lunch Seminar II: The class E and weak geodesic rays

    Location: MSRI: Simons Auditorium
    Speakers: Eleonora Di Nezza (Imperial College, London)

    The recent proof Demailly's conjecture by Witt Niströrm gives another evidence that pluripotential theory play a key role when working with complex Monge-Ampère equations in order to solve problems in differential and algebraic geometry. In this talk we investigate pluripotential tools: we characterize the
    Monge-Ampère energy class E in terms of "envelopes". And in order to do that, we develop the theory of weak geodesic rays in a big cohomogy class. We also give a positive answer to an open problem in pluripotential theory. This is a joint work with Tamas Darvas and Chinh Lu.

    Updated on Apr 15, 2016 09:15 AM PDT
  7. Postdoc Lunch Seminar I: Exotic nearly Kähler structures on the 6-sphere and the product of two 3-spheres

    Location: MSRI: Simons Auditorium
    Speakers: Lorenzo Foscolo (State University of New York, Stony Brook)

    Compact 6-dimensional nearly Kähler manifolds are the cross-sections of Riemannian cones with G2 holonomy. In particular they are Einstein manifolds with positive scalar curvature and admit real Killing spinors. Viewing Euclidean 7-space as the cone over the round 6-sphere endows the 6-sphere with a nearly Kähler structure which coincides with the standard G2-invariant almost complex structure induced by octonionic multiplication. A long-standing problem has been the question of existence of complete nearly Kähler 6-manifolds besides the four known homogeneous ones. We resolve this problem by proving the existence of an exotic (inhomogeneous) nearly Kähler structure on the 6-sphere and on the product of two 3-spheres. This is joint work with Mark Haskins, Imperial College London.


    Updated on Apr 15, 2016 09:14 AM PDT
  8. Postdoc Lunch Seminar II: A frame energy for immersed tori

    Location: MSRI: Simons Auditorium
    Speakers: Andrea Mondino (Universität Zürich)

    In the seminar I will present some joint work with T. Rivière where we study the Dirichlet energy of moving frames on 2-dimensional tori immersed in the euclidean $3\leq m$-dimensional space.  This functional, called Frame energy, is naturally linked to the Willmore energy of the immersion and on the conformal structure of the abstract underlying surface. I will discuss a ''Willmore Conjecture'' type lower bounds for such energy,  then I will introduce basic tools for doing the calculus of variations and finally I will give applications to regular homotopy classes of immersed tori in R^3.

    Updated on Apr 08, 2016 08:47 AM PDT
  9. Postdoc Lunch Seminar I: Conformal classes realizing the Yamabe invariant

    Location: MSRI: Simons Auditorium
    Speakers: Heather Macbeth (Massachusetts Institute of Technology)

    I will present an algebraic characterization of the conformal classes realizing a compact manifold’s Yamabe invariant (if any such classes exist). This characterization is a nonlinear analogue of an observation of Nadirashvili for metrics realizing the maximal first eigenvalue, and of an observation of Fraser and Schoen for metrics realizing the maximal first Steklov eigenvalue.

    Updated on Apr 08, 2016 08:45 AM PDT
  10. Postdoc Lunch Seminar I: Existence and deformations of singular Kahler-Einstein metrics

    Location: MSRI: Simons Auditorium
    Speakers: Chengjian Yao (Université Libre de Bruxelles)

    Donaldson's continuity method of deforming cone angles for conical Kahler-Einstein metrics is an important tool in the solution of the Yau-Tian-Donaldson conjecture. We give an alternative proof to the "openness" part of this method by smooth approximation, and generalize this idea to smoothable Q-Fano variety, which allows us to prove the existence and study the deformation of singular KE metrics.

    Updated on Mar 10, 2016 04:36 PM PST
  11. Postdoc Lunch Seminar I: Stratified spaces and the Yamabe problem

    Location: MSRI: Simons Auditorium
    Speakers: Ilaria Mondello (Institut de Mathématiques de Jussieu)

    Stratified spaces are singular metric spaces which have been introduced in topology, and then studied from an analytical point of view. They naturally appear in differential geometry as quotients or limits of smooth manifolds. In this talk I will briefly introduce the geometry of stratified spaces with the aim of illustrating the recent developments in the resolution of the Yamabe problem for this singular setting. In order to do this, I will show how some classical results of Riemannian geometry can be recovered by singular theorems for stratified spaces.

    Updated on Mar 04, 2016 09:18 AM PST
  12. Postdoc Lunch Seminar I: The conformal method on manifolds with ends of cylindrical type

    Location: MSRI: Simons Auditorium
    Speakers: Jeremy Leach (University of Washington)

    To find solutions for the Cauchy problem in general relativity, one must understand the set of solutions to the Einstein constraint equations. The conformal method has proved to be a very useful tool for parametrizing this set, and it has only recently found application on initial data sets with arbitrary mean curvature. In this talk, I will outline the conformal method and describe my recent work in extending this technique to manifolds with asymptotically conformally cylindrical ends.

    Updated on Feb 18, 2016 04:05 PM PST
  13. Postdoc Lunch Seminar II: Riemannian manifolds with positive Yamabe invariant and Paneitz operator

    Location: MSRI: Simons Auditorium
    Speakers: Yueh-Ju Lin (University of Michigan)

    For a compact Riemannian manifold of dimension at least three, we know that positive Yamabe invariant implies the existence of a conformal metric with positive scalar curvature. As a higher order analogue, we seek for similar characterizations for the Paneitz operator and Q-curvature in higher dimensions. For a smooth compact Riemannian manifold of dimension at least six, we prove that the existence of a conformal metric with positive scalar and Q-curvature is equivalent to the positivity of both the Yamabe invariant and the Paneitz operator. In addition, we also study the relationship between different conformal invariants associated to the Q-curvature. This is joint work with Matt Gursky and Fengbo Hang.

    Updated on Feb 11, 2016 01:37 PM PST
  14. Postdoc Lunch Seminar I: Sharp Trace-Sobolev inequalities of order 4

    Location: MSRI: Simons Auditorium
    Speakers: Antonio Ache (Princeton University)

    We establish sharp Sobolev inequalities of order four on Euclidean d-balls for d greater than or equal to four. When d=4, our inequality generalizes the classical second order Lebedev-Milin inequality on Euclidean 2-balls. Our method relies on the use of scattering theory on hyperbolic d-balls. As an application, we characterize the extremals of the main term in the log-determinant formula corresponding to the conformal Laplacian coupled with the boundary Robin operator on Euclidean 4-balls.  This is joint work with Alice Chang.

    Updated on Feb 11, 2016 01:39 PM PST
  15. Postdoc Lunch Seminar II: Positive sectional curvature and torus symmetry

    Location: MSRI: Simons Auditorium
    Speakers: Lee Kennard (University of Oklahoma)

    It is a classical question to examine which smooth manifolds admit Riemannian metrics with positive/non-negative sectional curvature. In this talk, I will discuss some joint work with Manuel Amann on this question in the presence of torus symmetry, specifically in small dimensions. It extends work of Dessai, where a number of topological invariants of 8-manifolds with positive curvature and torus symmetry are calculated, both in general and under additional assumptions (e.g., rationally elliptic or homogeneous).

    Updated on Jan 29, 2016 09:39 AM PST
  16. Postdoc Lunch Seminar I: Positively curved Ricci expanders

    Location: MSRI: Simons Auditorium
    Speakers: Alix Deruelle (Université de Paris VI (Pierre et Marie Curie)-Université de Paris XI (Paris-Sud))

    Gradient Ricci expanding solitons are immortal self-similarities to the Ricci flow. We will focus on the possibility of resolving metric cones over a smooth compact manifold by such expanders. More precisely, we will start by giving examples confirming these expectations then we will concentrate on asymptotic estimates, compactness phenomena, and deformations of conical Ricci expanders.

    Updated on Jan 29, 2016 09:38 AM PST
  17. Postdoc Symposium (Part I): Long-Time Existence of Schrodinger Equations with Mixed Signature

    Location: MSRI: Simons Auditorium
    Speakers: Nathan Totz (University of Massachusetts Amherst)

    After a brief review of full justification of model equations, we present an application of model justification to the long-time
    well-posedness of the cubic "hyperbolic" NLS equation, in which the Laplacian is replaced by an indefinite second order operator-- and for which the long-time existence remains open for large data due to the absence of a coercive Hamiltonian.

    Updated on Dec 02, 2015 08:44 AM PST
  18. Postdoc Symposium (Part II): Front Propagation and Symmetrization in the Nonlocal Fisher-KPP Equation

    Location: MSRI: Simons Auditorium
    Speakers: Andrei Tarfulea (University of Chicago)

    We prove strong gradient decay estimates for solutions to the multi-dimensional Fisher-KPP equation with fractional diffusion. It is known that this equation exhibits exponentially advancing level sets with strong qualitative upper and lower bounds on the solution. However, little has been shown concerning the gradient of the solution. We prove that, under mild conditions on the initial data, the first and second derivatives of the solution obey a comparative exponential decay in time. We then use this estimate to prove a symmetrization result, which shows that the reaction front circularizes in renormalized coordinates.

    Updated on Nov 13, 2015 09:31 AM PST
  19. Postdoc Symposium (Part I): Large scale behaviour of phase coexistence models

    Location: MSRI: Simons Auditorium
    Speakers: Weijun Xu (University of Warwick)

    The solutions to many singular SPDEs are obtained as limits of regularised and then renormalised equations. The renormalisation changes the "original" equation via quantities that are typically infinity, but they do have concrete physical meanings. As an example, I will discuss how the Phi^4_3 equation, interpreted after suitable renormalisations, arise naturally as the universal limit of symmetric phase coexistence models. We will also see how this universality can be lost when symmetry is broken.

    Updated on Nov 13, 2015 09:30 AM PST
  20. Postdoc Symposium (Part II): Poincar\'e inequalities and noncommutative martingales

    Location: MSRI: Simons Auditorium
    Speakers: Qiang Zeng (MSRI - Mathematical Sciences Research Institute)

    Poincar\'e inequalities are among the most studied inequalities in probability and functional analysis. In this talk we will discuss the $L_p$ Poincar\'e inequalities with constants $C\sqrt{p}$. They are weaker than the log-Sobolev inequality, but still imply subgaussian concentration and transportation cost inequalities. We use martingale methods and infinite dimensional Brownian motions to prove these inequalities in various contexts, and demonstrate that certain noncommutative techniques are helpful even in some commutative settings.

    Updated on Nov 06, 2015 04:25 PM PST
  21. Postdoc Symposium (Part I): Enhanced lifespan methods for nonlinear evolutions

    Location: MSRI: Simons Auditorium
    Speakers: Mihaela Ifrim (University of California, Berkeley)

    The first part of my talk will discuss ways of establishing cubic lifespan bounds for quasi-linear dispersive equations via the \emph{modified energy method}. This robust method is an upgrade of the normal form energy method introduced by Shatah in 1983 for the Klein-Gordon equation. For simplicity we will first implement it for the Burger's-Hilbert equation (which is not dispersive), but where it nevertheless works.  The second part of my talk will discuss global existence of solutions provided that the initial data is small and spatially localized via the \emph{testing with wave packets method}. We will show how it works  for one simple example: for the one dimensional cubic NLS.

    Updated on Nov 06, 2015 04:24 PM PST
  22. Postdoc Symposium (Part II) - The log-Sobolev inequality for unbounded spin systems

    Location: MSRI: Simons Auditorium
    Speakers: Georg Menz (University of California, Los Angeles)

     The log-Sobolev inequality (LSI) is a very useful tool for analyzinghigh-dimensional situations. For example, the LSI can be used for deriving hydrodynamic limits, for estimating the error in stochastic homogenization, for deducing upper bounds on the mixing times of Markov chains, and even in the proof of the Poincaré conjecture by Perelman. For most applications, it is crucial that the constant in the LSI is uniform in the size of the underlying system. In this talk, we
    discuss when to expect a uniform LSI  in the setting of unbounded spin systems. We will also explain a connection to the KLS conjecture.

    Updated on Oct 30, 2015 09:26 AM PDT
  23. Postdoc Symposium (Part I) - Wave maps on hyperbolic spaces

    Location: MSRI: Simons Auditorium
    Speakers: Sohrab Shahshahani (University of Michigan)

    The wave maps equation is an important example of a geometric wave equation, and generalizes the concept of a free wave to manifold-valued maps. There has been significant progress on understanding the dynamics of wave maps from the Minkowski space to both positively and negatively curved targets, especially in the energy critical setting where the spatial domain dimension is two. In this talk I will discuss some of the new behaviors which result from changing the domain geometry. In particular, I will give a survey of recent works with Andrew Lawrie and Sung-Jin Oh in the case where the domain is the hyperbolic space.

    Updated on Oct 30, 2015 09:25 AM PDT
  24. Postdoc Symposium (Part II): Scattering for intercritical NLS

    Location: MSRI: Simons Auditorium
    Speakers: Jason Murphy (University of California, Berkeley)

    We review the subcritical scattering theory for intercritical NLS.  Specifically, we consider defocusing power-type nonlinear Schr\"odinger equations with a nonlinearity that is mass-supercritical and energy-subcritical and give a proof of scattering for solutions with data in H^1.  The talk will be primarily expository and is meant to serve as an introduction to Morawetz estimates. 

    Updated on Oct 09, 2015 03:51 PM PDT
  25. Postdoc Symposium (Part I): Path-by-path uniqueness of solutions of stochastic heat equation with a drift

    Location: MSRI: Simons Auditorium
    Speakers: Oleg Butkovsky (Technion---Israel Institute of Technology)

    It is well known from the results of A.Zvonkin, A.Veretennikov, N.Krylov, A.Davie, F.Flandoli, J.Mattingly and other probabilists that ordinary differential equations (ODEs) regularize in the presence of noise. Even if an ODE is "very bad" and has no solutions (or has many solutions), then the addition of a random noise leads (almost surely) to a "nice" ODE with a unique solution.  We investigate the same phenomenon for a heat equation with a drift. We prove that for almost all trajectories of random white noise the perturbed heat equation has a unique solution (even if the original heat equation with a drift had many or no solutions).(Joint work with Leonid Mytnik.)

    Updated on Oct 09, 2015 03:46 PM PDT
  26. Postdoc Symposium (Part II): Inverse boundary value problems

    Location: MSRI: Simons Auditorium
    Speakers: Boaz Haberman (University of Chicago)

    A fundamental problem in PDE is to determine the coefficients of a system from physical measurements. I will introduce the problem of recovering a magnetic Schrodinger operator from the boundary data of solutions and discuss some connections to dispersive PDE. 

    Updated on Oct 01, 2015 01:38 PM PDT
  27. Postdoc Symposium (Part I): Observability Inequality of Backward Stochastic Heat Equations for Measurable Sets and Its Applications

    Location: MSRI: Simons Auditorium
    Speakers: Jie Zhong (University of Central Florida)

    We will provide a direct proof of the observability inequality of backward stochastic heat equations for measurable sets. As an immediate application, the null controllability of the forward heat equations is obtained. Moreover, an interesting relaxed optimal actuator location problem is formulated, and the existence of its solution is proved. Finally, the solution is characterized by a Nash equilibrium of the associated game problem.

    Updated on Oct 01, 2015 01:38 PM PDT
  28. Postdoc Symposium (Part II): Stochastic heat equation with general Gaussian noises

    Location: MSRI: Simons Auditorium
    Speakers: Jingyu Huang (University of Utah)

    We study the stochastic heat equation with multiplicative noises: $\frac {\partial u }{\partial t} =\frac  12 \Delta u  + u \dot{W}$, where $\dot W$ is a mean zero Gaussian noise and $u \dot{W}$ is interpreted  both in the sense of Skorohod and Stratonovich. The existence and uniqueness of the solution are studied for noises with general time and spatial covariance structure. Feynman-Kac formulas for the solutions and for the moments of the solutions are obtained under general and different conditions. These formulas are applied to obtain the H\"older continuity of the solutions. They are also applied to obtain the intermittency bounds for the moments of the solutions.

    Updated on Sep 25, 2015 11:04 AM PDT
  29. Postdoc Symposium (Part II): Nonlinear noise excitation, Intermittency and Multifractality

    Location: MSRI: Simons Auditorium
    Speakers: Kunwoo Kim (Technion---Israel Institute of Technology)

    Intermittency usually refers to something occurring irregularly at different scales or tall peaks on small regions, typically as time gets larger.

    In the first part of this talk, instead of looking at a large time behavior, we will consider nonlinear noise excitation of a large family of intermittent stochastic partial differential equations (SPDEs). We show that there is a near-dichotomy: “Semi-discrete” equations are nearly always far less excitable than “continuous” equations.

    In the second part of this talk, we consider large scale structures of points of tall peaks for various SPDEs such as parabolic Anderson models (which are intermittent) and SPDEs with additive noise (which are not intermittent). We show that parabolic Anderson models are multi-fractal (as expected), but so are SPDEs with additive noise.

    This is based on joint works with Davar Khoshnevisan and Yimin Xiao.

    Updated on Sep 18, 2015 11:34 AM PDT
  30. Postdoc Symposium (Part II): Linear inviscid damping for monotone shear flows

    Location: MSRI: Simons Auditorium
    Speakers: Christian Zillinger (Universität Bonn)

    Recently there has been much interest in damping phenomena for kinetic equations following the seminal works of Mouhot-Villani on Landau damping and of Bedrossian-Masmoudi on inviscid damping around Couette flow.
    In this talk I present some of the main results of my PhD thesis on linear inviscid damping for the 2D Euler equations around general monotone shear  flows in the framework of Sobolev regularity.
    Here I consider both the settings of an infinite periodic channel and a finite periodic channel with impermeable walls.
    The latter setting is shown to not only be technically more challenging, but to exhibit qualitatively different behavior due to boundary effects.

    Updated on Sep 10, 2015 08:56 AM PDT
  31. Postdoc Symposium (Part I): Bubbling analysis for energy critical geometric wave equations

    Location: MSRI: Simons Auditorium
    Speakers: Sung-Jin Oh (University of California, Berkeley)
    A powerful strategy for establishing regularity in a non-perturbative setting is to combine bubbling analysis with a rigidity argument. Assuming that a blow up occurs, one first magnifies near the blow up and identifies a nontrivial profile (bubbling analysis). Then one starts proving special properties of this profile, to the point such an object cannot exist and one arrives at a contradiction (rigidity). 
    The goal of this talk is to describe a bubbling analysis scheme for energy critical wave equations introduced by J. Sterbenz and D. Tataru (in the context of the critical wave map equation), which is robust yet highly effective. I will begin by briefly describing my recent work with D. Tataru on the energy critical Maxwell-Klein-Gordon (MKG) equation, where we followed this scheme to establish global well-posedness and scattering for arbitrary finite energy data. I will then illustrate the scheme by considering a simple model equation, namely the cubic NLW on the 4+1-dimensional Minkowski space, which resembles MKG but is largely free of technical difficulties.
    Updated on Sep 10, 2015 08:55 AM PDT
  32. Postdoc Symposium (Part II) - Small Divisors and the NLSE

    Location: MSRI: Simons Auditorium
    Speakers: Bobby Wilson (Massachusetts Institute of Technology)

    We will discuss the classical small divisor problem, and connections to questions concerning Sobolev stability of solutions to the nonlinear Schrodinger equation on the d-dimensional torus. In particular, we will examine results concerning the arbitrarily long-time orbital stability of plane wave solutions under generic perturbations.

    Created on Aug 28, 2015 02:33 PM PDT
  33. Postdoc Symposium (Part I) - Initial and boundary value problems for the deterministic and stochastic Zakharov-Kuznetsov equation in a bounded domain

    Location: MSRI: Simons Auditorium
    Speakers: Chuntian Wang (University of California, Los Angeles)
    In this talk I will focus on the well-posedness and regularity of the Zakharov- Kuznetsov (ZK) equation in the deterministic and stochastic cases, subjected to a rectangular domain in space dimensions 2 and 3. ZK equation is a multi-dimensional extension of the KdV equation.  
    Mainly we have established the existence, in 3D, and uniqueness, in 2D, of the weak solutions, and the local and global existence of strong solutions in 3D. Then we extend the results to the stochastic case and obtain in 3the existence of martingale solutions, and in 2the pathwise uniqueness and existence of pathwise solutions. The main focus is on the mixed features of the partial hyperbolicity, nonlinearity, nonconventional boundary conditions,anisotropicity and stochasticity, which requires methods quite different than those of the classical models in fluid dynamics, such as the Navier-Stokes equation, Primitive Equation and related equations.
    Created on Aug 28, 2015 02:31 PM PDT
  34. GAAHD Postdoc Seminar: Diophantine approximation in Lie groups

    Location: MSRI: Simons Auditorium
    Speakers: Nicolas de Saxce (Université de Paris XIII (Paris-Nord))

    We will study the diophantine properties of random finitely generated subgroups of Lie groups, focusing mainly on the case of nilpotent Lie groups.

    Updated on May 01, 2015 12:21 PM PDT
  35. DMS Postdoc Seminar: Bounded cohomology of mapping class groups (and acylindrically hyperbolic groups)

    Location: MSRI: Simons Auditorium
    Speakers: Maria Beatrice Pozzetti (University of Warwick)

    Bounded cohomology is a variation of usual cohomology that has many interesting geometric applications: for example it allows to define interesting invariants on some character varieties, and select maximal representations. However it is in general very difficult to compute and still poorly understood.

    I will discuss in which sense mapping class groups have enough hyperbolic features to ensure that their third bounded cohomology is infinite dimensional. This is joint work with Roberto Frigerio and Alessandro Sisto.

    Updated on Apr 24, 2015 03:26 PM PDT
  36. GAAHD Postdoc Seminar: Hausdorff dimension of product sets

    Location: MSRI: Simons Auditorium
    Speakers: Nicolas de Saxce (Université de Paris XIII (Paris-Nord))

    Given a subset A of a group G, we want to compare the size the product set AAA of elements that can be written as products of three elements of A with the size of A. I will discuss this problem when G is a simple Lie group and the sets A and AAA are measured by their Hausdorff dimension.

    Updated on Apr 17, 2015 10:00 AM PDT
  37. DMS Postdoc Seminar: An Overview of the Nahm Transform

    Location: MSRI: Simons Auditorium
    Speakers: Andres Larrain-Hubach (University of Arizona)

    The Nahm Transform is a nonlinear analog of the Fourier Transform, used to construct maps between moduli spaces of solutions of dimensional reductions of Yang-Mills equations. I will discuss several examples and open problems related  to this construction, focusing on the moduli space of solutions to Hitchin equations over a Riemann surface. 

    Updated on Apr 17, 2015 10:38 AM PDT
  38. GAAHD Postdoc Seminar: Small generators of integral orthogonal groups

    Location: MSRI: Simons Auditorium
    Speakers: Han Li (Wesleyan University)

    In 1940 Siegel proved that for any indefinite integral quadratic form the integral points of its orthogonal group is finitely generated. The aim of this talk is to present an effective upper bound on the norm of a finite generating set. This is a joint work with Professor Gregory A. Margulis, and the proof uses our recent work on the equivalence of integral quadratic forms.

    Updated on Apr 03, 2015 11:08 AM PDT
  39. DMS Postdoc Seminar: Parametrizing Hitchin components

    Location: MSRI: Simons Auditorium
    Speakers: Guillaume Dreyer (University of Notre Dame)

    Given a geodesic lamination with finitely many leaves in a closed surface of genus at least 2, I'll construct a very explicit parametrization of the Hitchin component of this surface. In essence, this parametrization is an extension of Thurston's shearing coordinates for the Teichmueller space of a closed surface, combined with Fock-Goncharov's coordinates for the moduli space of positive framed local systems of a punctured surface. This is joint work with Francis Bonahon.

    Updated on Apr 03, 2015 10:33 AM PDT
  40. GAAHD Postdoc Seminar: The stable type of the mapping class group and some relatively hyperbolic groups and applications to pointwise ergodic averages

    Location: MSRI: Simons Auditorium
    Speakers: Ilya Gekhtman (Rheinische Friedrich-Wilhelms-Universität Bonn)

    The stable ratio set of a nonsingular action is a notion introduced by Bowen and Nevo to prove pointwise ergodic theorems for measure preserving actions of certain nonamenable groups.

    I  prove that stable ratio set of the action of a discrete subgroup of isometries of a CAT(-1) space with finite Bowen-Margulis measure on its boundary with the Patterson-Sullivan measure has numbers other than 0, 1 and \infinity, extending techniques of Bowen from the setting of hyperbolic groups.

    I also prove the same result for the action of the mapping class group on the sphere of projective measured foliations with the Thurston measure, using some "statistical hyperbolicity" properties for the (non hyperbolic) Teichmueller metric on Teichmueller space.

    Updated on Mar 26, 2015 03:44 PM PDT
  41. DMS Postdoc Seminar: Coupled Hitchin Equations

    Location: MSRI: Simons Auditorium
    Speakers: Qiongling Li (Rice University)

    In this talk, I will talk about a technical part in the joint paper with Brian Collier about studying asymptotic behavior of Hitchin representations in terms of Higgs bundles. This technical part estimates the asymptotic solution of the coupled Hitchin equations. I will also discuss how the analysis is related to geometry of frames.

    Updated on Mar 26, 2015 04:14 PM PDT
  42. GAAHD Postdoc Seminar: Gap distributions for saddle connections on the octagon

    Location: MSRI: Simons Auditorium
    Speakers: Grace Work (University of Illinois at Urbana-Champaign)

    (Joint with Caglar Uyanik.) Following a strategy developed by Athreya and Cheung, we compute the gap distribution of the slopes of saddle connections on the octagon by translating the problem to a question about return times of the horocycle flow to an appropriate Poincaré Section. This same strategy was used by Athreya, Chaika, and Lelièvre to compute the gap distribution on the Golden L. The octagon is the first example of this type of computation where the Veech group has two cusps.

    Created on Mar 20, 2015 12:00 PM PDT
  43. DMS Postdoc Seminar: Andreev's theorem on projective Coxeter polyhedra

    Location: MSRI: Simons Auditorium
    Speakers: Gye-Seon Lee (Ruprecht-Karls-Universität Heidelberg)

    In 1970, E.M. Andreev gave a full description of 3-dimensional compact hyperbolic polyhedra with dihedral angles submultiples of pi. We call them hyperbolic Coxeter polyhedra. More precisely, given a combinatorial polyhedron C with assigned dihedral angles, Andreev’s theorem provides necessary and sufficient conditions for the existence of a hyperbolic Coxeter polyhedron realizing C. Since hyperbolic geometry arises naturally as sub-geometry of real projective geometry, we can ask an analogous question for compact real projective Coxeter polyhedra. In this talk, I’ll give a partial answer to this question. This is a joint work with Suhyoung Choi.

    Created on Mar 20, 2015 11:57 AM PDT
  44. GAAHD Postdoc Seminar: Sparse equidistribution under a unipotent flow

    Location: MSRI: Baker Board Room
    Speakers: Cheng Zheng (Ohio State University)

    We consider the orbits {pu(n^{1+γ})|n ∈ N} in Γ\PSL(2,R), where Γ is a non-uniform lattice in PSL(2,R) and u(t) is the standard unipotent group in PSL(2,R). Under a Diophantine condition on the intial point p, we show that {pu(n^{1+γ})|n ∈ N} is equidistributed in Γ\PSL(2,R) for small γ>0, which generalizes a result of Venkatesh.

    Created on Mar 05, 2015 04:18 PM PST
  45. DMS Postdoc Seminar: Degeneration of complex projective structures on surfaces that converges in the character variety

    Location: MSRI: Baker Board Room
    Speakers: Shinpei Baba (Ruprecht-Karls-Universität Heidelberg)

    A complex projective structure is a geometric structure on a surface modeled on the Riemann sphere. Then a complex projective structure has a holonomy representation from the fundamental group of the surface into PSL(2, C), which is not necessarily discrete.

    We discuss about ``neck-pinching'’ type degeneration of complex projective structures when their holonomy representations converge in the character variety.

    Created on Mar 05, 2015 04:20 PM PST
  46. GAAHD Postdoc Seminar: Hausdorff dimension of divergent trajectories under the diagonal geodesic flow on product space of hyperbolic spaces

    Location: MSRI: Simons Auditorium
    Speakers: Lei Yang (Hebrew University)
    In this talk, we will study the behavior of trajectories of diagonal geodesic flow on product space of k copies of n-dimensional non-compact hyperbolic spaces with finite volume,  and shall show that the Hausdorff dimension of the collection of divergent trajectories is equal to k(2n-1)-\frac{n-1}{2}. This extends a result of Yitwah Cheung.
    Updated on Feb 27, 2015 12:18 PM PST
  47. DMS Postdoc Seminar: MCG actions on character varieties

    Location: MSRI: Simons Auditorium
    Speakers: Sara Maloni (Brown University)
    In this talk we consider the SL(2,C)-character variety X=Hom(F_3, SL(2,C))//SL(2,C) of the free group F_3 of rank 3. We will consider F_3 as the fundamental group of two different surfaces: the four-holed sphere S, and of the three-holed punctured plane N. We will consider the action of the mapping class groups MCG(S) and MCG(N) on it. In particular, we describe a domain of discontinuity for these actions on the relative character varieties X_rel(S) and X_rel(N), which  are the set of representations for which the traces of the boundary curves are fixed. Time permitting, we will mention some open questions on which we are working on now.
    (Part of this is joint work with F. Palesi and S. P. Tan, and part is work in progress with F. Palesi.)
    Updated on Feb 27, 2015 02:05 PM PST
  48. GAAHD Postdoc Seminar: Generalizations of Furstenberg's x2 x3 theorem

    Location: MSRI: Simons Auditorium
    Speakers: Asaf Katz (Hebrew University)

    In his seminal paper from 1967, Furstenberg proved that for every irrational x, the set 2^{n}3^{m}x is dense modulo 1.
    I will show a couple of generalizations of this result, which imply density of much sparser sequences, using earlier works of D. Meiri and M. Boshernitzan, following the proof of Bourgain-Lindenstrauss-Michel-Venkatesh.

    Updated on Feb 20, 2015 09:13 AM PST
  49. DMS Postdoc Seminar: Splittings, suspension flows, and polynomials for free-by-cyclic groups

    Location: MSRI: Simons Auditorium
    Speakers: Spencer Dowdall (Vanderbilt University)

    The semi-direct product of a finite-rank free group with the integers can often be expressed as such a product in infinitely many ways. This talk will explore this phenomenon and work towards 1) describing the structure of the family of such splittings of a given group, and 2) looking for for relationships between the splittings themselves. Along the way, we'll study dynamical systems ranging from graph maps and cross sections of semi-flows to newly introduced polynomial invariants tying these all together. Time permitting, I'll discuss geometric properties of more general free group extensions. This represents work with Ilya Kapovich and Christopher Leininger, and separately with Samuel Taylor.

    Updated on Feb 20, 2015 09:36 AM PST
  50. GAAHD Postdoc Seminar: Pointwise equidistribution for one-parameter diagonal group action on $X=SL_n(\mathbb R)/SL_n(\mathbb Z)$

    Location: MSRI: Simons Auditorium
    Speakers: Ronggang Shi (Tel Aviv University)

    Let $F=\{g_t\}$ be a one-parametr diagonal subgroup of $SL_n(\mathbb R)$.
    We assume  $F$ has no nonzero invariant vectors in $\mathbb R^n$.
    Let $x\in X, \varphi\in C_c(X)$ and $\mu$ be the probability Haar measure
    on $X$. For certain proper subgroup $U$ of the unstable horospherical  subgroup
    of $g_1$ we show that for almost every $u\in U$
    \frac{1}{T}\int_0^T\varphi({g_tux})dt \to \int_X\varphi d\mu.
    If $\varphi$ is moreover smooth, we can get an  error rate of the convergence.
    The error rate is ineffective due to the use of Borel-Cantelli lemma.

    Updated on Feb 13, 2015 11:12 AM PST
  51. DMS Postdoc Seminar: Algebraic structure and topology of homeomorphism groups

    Location: MSRI: Simons Auditorium
    Speakers: Kathryn Mann (University of California, Berkeley)

    To what extent does the algebraic structure of a topological group determine its topology?  Many (but not all!) examples of real Lie groups G have a unique Lie group structure, meaning that every abstract isomorphism G -> G is necessarily continuous.  

    In this talk, I'll show a strictly stronger result for groups of homeomorphisms of manifolds: every abstract homomorphism from Homeo(M) to any other separable topological group is necessarily continuous.  

    Along the way, I'll introduce some beautiful and classical properties of groups of homeomorphisms.  This talk should be accessible to everyone.  

    Updated on Feb 13, 2015 11:10 AM PST
  52. GAAHD Postdoc Seminar: Almost-Fuchsian space and entropy of minimal surfaces

    Location: MSRI: Simons Auditorium
    Speakers: Andrew Sanders (University of Illinois at Chicago)

    An almost-Fuchsian manifold is a quasi-Fuchsian manifold which contains an incompressible minimal surface with principal curvatures less than one everywhere.  The topological entropy of the geodesic flow on the minimal surface defines a function on the space of almost-Fuchsian manifolds.  We will explain how this function can be used to give a metric on Fuchsian space.  Furthermore, we will also discuss the relationship between this entropy and the Hausdorff dimension of limit sets of quasi-Fuchsian groups.

    Updated on Feb 05, 2015 11:45 AM PST
  53. DMS Postdoc Seminar: Quantum ergodicity and averaging operators on the sphere

    Location: MSRI: Simons Auditorium
    Speakers: Etienne Le Masson (Hebrew University)

    The quantum ergodicity theorem says that on a compact Riemannian manifold with ergodic geodesic flow, for any orthonormal basis of eigenfunctions of the Laplacian in L2, the modulus squared of these eigenfunctions converge weakly as probability measures to the uniform measure, in the limit of large eigenvalues and up to a subsequence of density 0.
    On the sphere the geodesic flow is not ergodic and it is possible to find subsequences of eigenfunctions with positive density that do not satisfy the conclusion of the theorem. However, it holds almost surely for random eigenbasis.
    We will present a quantum ergodicity theorem on the sphere for joint eigenfunctions of the Laplacian and an averaging operator over a finite set of rotations. The proof is based on a new argument for quantum ergodicity on regular graphs.

    Updated on Feb 05, 2015 04:21 PM PST
  54. GRT Pizza Seminar

    Location: MSRI: Simons Auditorium
    Speakers: Paul Hamacher (TU München)
    Updated on Sep 03, 2014 04:22 PM PDT
  55. GRT Pizza Seminar: Representations of quivers over a finite field

    Location: MSRI: Simons Auditorium
    Speakers: Galyna Dobrovolska (Columbia University)

    The Kac polynomial counts the number of representations of a quiver over a finite field which are indecomposable over the algebraic closure of this field. Recently Hausel, Letellier, and Rodriguez-Villegas proved the Kac conjecture which states that the coefficients of the Kac polynomial are nonnegative. I will talk about this and related results.

    Updated on Nov 07, 2014 11:15 AM PST
  56. NGM Pizza Seminar: Hyperelliptic curves, local character expansions, and endoscopy

    Location: MSRI: Simons Auditorium
    Speakers: Cheng-Chiang Tsai (Harvard University)

    A representation of a reductive p-adic group has its character as a distribution on the group. Its asymptotic behavior near the identity is given by a finite-term local character expansion of Harish-Chandra. In this talk, we state a result giving a few terms in the local character expansions for certain supercuspidal representations of a ramified unitary group. The numbers are related to the number of rational points on certain covers of hyperelliptic curves. We'll then talk about how endoscopy transfer for these characters is related to geometric identities regarding H^1 of these curves. A side goal will be to demonstrate possible similarity between such phenomenon and the work of Bhargava-Gross on arithmetic invariant theory of $SO_{2n+1}$ on $\text{Sym}^2$.

    Updated on Nov 04, 2014 04:18 PM PST
  57. GRT Pizza Seminar: The geometry of G-bundles on an elliptic curve and spherical Eisenstein sheaves

    Location: MSRI: Simons Auditorium
    Speakers: Dragos Fratila (Université de Paris VII (Denis Diderot))

    I will present some results about the geometry of the stack of G-bundles on an elliptic curve and how one can use this to construct simple summands of spherical Eisenstein sheaves. If time permits I will discuss a conjectural description of all the simple summands of spherical Eisenstein sheaves.

    Updated on Oct 31, 2014 11:02 AM PDT
  58. NGM Pizza Seminar: The eigencurve is proper

    Location: MSRI: Simons Auditorium
    Speakers: Hansheng Diao (Institute for Advanced Study)

    The eigencurve is a rigid analytic curve over Q_p parametrizing all finite slope overconvergent modular eigencurve. It is a conjecture of Coleman-Mazur that the eigencurve has "no holes". In other words, the eigencurve is proper over the weight space. We prove that the conjecture is true.

    Updated on Oct 30, 2014 10:10 AM PDT
  59. GRT Pizza Seminar: Hitchin-Frenkel-Ngô's fibration and Vinberg semigroup

    Location: MSRI: Simons Auditorium
    Speakers: Alexis Bouthier (Université de Paris XI)

    In this talk, we will explain the link between the Vinberg's semigroup and the Hitchin group like fibration, that was introduced by Frenkel and Ngô for SL_{2}. This fibration appears as a nice object to get orbital integrals for the spherical Hecke algebra and a good understanding of the orbital side of the trace formula.

    Updated on Oct 24, 2014 02:40 PM PDT
  60. NGM Pizza Seminar: Control theorems for overconvergent automorphic forms

    Location: MSRI: Simons Auditorium
    Speakers: Christian Johansson (University of Oxford)

    A theorem of Coleman asserts that if f is an overconvergent U_p-eigenform of weight k>1 such that the valuation of its U_p-eigenvalue is <k-1, then f is classical modular form. In this talk I will discuss variations of Coleman's proof of this theorem, with an eye towards ideas that generalize to higher-dimensional Shimura varieties. Part of this is joint work with Vincent Pilloni.

    Updated on Oct 23, 2014 09:18 AM PDT
  61. NGM Pizza Seminar: Level raising mod 2 and 2-Selmer groups

    Location: MSRI: Simons Auditorium
    Speakers: Bao Le Hung (University of Chicago)

    We discuss a level raising result mod p=2 for weight 2 modular forms, where some extra phenomena happens compared to the p odd case. We then apply this to study 2-Selmer groups of modular forms in level raising families.

    This is joint work with Chao Li.

    Updated on Oct 23, 2014 09:15 AM PDT
  62. GRT Pizza Seminar: Beilinson-Drinfeld's construction of automorphic D-modules

    Location: MSRI: Simons Auditorium
    Speakers: Sam Raskin (Massachusetts Institute of Technology)

    We're going to try and describe the ideas that go into Beilinson and Drinfeld's main construction from their book "Quantization of Hitchin's integrable system and Hecke eigensheaves."

    Created on Oct 23, 2014 05:01 PM PDT
  63. GRT Pizza Seminar: Monodromy representations of braid groups.

    Location: MSRI: Simons Auditorium
    Speakers: Yaping Yang (MSRI - Mathematical Sciences Research Institute)

    I will discuss a class of integrable connections associated to root systems and describe their monodromy in terms of quantum groups. These connections come in three forms, rational form, trigonometric form, and the elliptic form, which lead to representations of braid groups, affine braid groups, and elliptic braid group respectively.

    For the rational connection, I will discuss in detail two concrete incarnations: the (Coxeter) Knizhnik-Zamolodchikov connection and the Casimir connection.

    The first takes values in the Weyl group W. Its monodromy gives rise to an isomorphism between the Hecke algebra (with generic parameters) of W and the group algebra C[W] of the Weyl group. The second is associated to the semisimple Lie algebra g, and takes values in the universal enveloping algebra of g. Its monodromy is described by the quantum Weyl group operators of the quantum group. The trigonometric and the elliptic analog will also be discussed.

    The elliptic part is joint work with Valerio Toledano Laredo.

    Updated on Oct 09, 2014 03:55 PM PDT
  64. NGM Pizza Seminar: Generic smoothness for G-valued potentially semi-stable deformation rings

    Location: MSRI: Simons Auditorium
    Speakers: Rebecca Bellovin

    Kisin showed that the generic fibers of potentially semi-stable (framed) deformation rings of p-adic Galois representations valued in GL_n are generically smooth, and he computed their dimensions.  I will explain how to extend these results to Galois representations valued in an arbitrary connected reductive group G.  If time permits, I will give an example showing that the corresponding schemes can have singular components.  The key tool is the geometry of the nilpotent cone.

    Updated on Oct 09, 2014 09:40 AM PDT
  65. GRT Pizza Seminar

    Location: MSRI: Simons Auditorium
    Updated on Sep 03, 2014 03:44 PM PDT
  66. GRT Pizza Seminar: Flying rings and the Kashiwara-Vergne problem

    Location: MSRI: Simons Auditorium
    Speakers: Zsuzsanna Dancso (MSRI - Mathematical Sciences Research Institute)

    I will present a sketch of a topological proof of the Kashiwara-Vergne problem in Lie theory. This is a special case of a general method which provides several interesting examples of close relationships between quantum topology and algebra, in particular equations in graded spaces.

    Updated on Sep 26, 2014 10:45 AM PDT
  67. NGM Pizza Seminar: Weyl's law for automorphic forms and Hecke operators

    Location: MSRI: Simons Auditorium
    Speakers: Jasmin Matz (Rheinische Friedrich-Wilhelms-Universität Bonn)

    A theorem of Weyl asserts that the number of eigenvalues of the Laplacian less than X on a compact Riemann surface of dimension d is asymptotic to a constant multiple of X^{d/2}. A similar statement is true for the number of cuspidal automorphic representations with bounded infinitesimal character of G(\R)/K for G a split adjoint semisimple group and K a maximal compact subgroup of G(\R) (Selberg, Miller, Müller, Lindenstrauss-Venkatesh). Instead of just counting automorphic forms, it is also of interest to weight this counting by traces of Hecke operators. An asymptotic for this problem together with a bound on the error term has applications in the theory of families of L-functions. I want to explain the automorphic Weyl law, and some recent results for the problem involving Hecke operators in the case of GL(n).

    Updated on Sep 25, 2014 12:52 PM PDT
  68. NGM Pizza Seminar: Description of the Moduli Space for U(n,0) as a Tensor Product of Categories.

    Location: MSRI: Simons Auditorium
    Speakers: Zavosh Amir-Khosravi (Fields Institute for Research in Mathematical Sciences)

    Shimura varieties attached to unitary groups of signature (n-r,r) have integral models described by moduli spaces of certain principally polarized abelian schemes. We will consider the case r=0, and show that the corresponding moduli stack can be described as a categorical tensor product of the stack of CM elliptic curves with a category of rank-n positive-definite hermitian modules.

    Updated on Sep 19, 2014 10:04 AM PDT
  69. GRT Pizza Seminar

    Location: MSRI: Simons Auditorium
    Updated on Sep 03, 2014 03:37 PM PDT
  70. NGM Pizza Seminar: The p-adic Gross-Zagier formula on Shimura curves.

    Location: MSRI: Simons Auditorium
    Speakers: Daniel Disegni (McGill University)

    For elliptic curves E/Q whose L-function L=L(E,s) vanishes to order one at s=1, the rank of E(Q) is also known to be one. This is the first prediction of the Birch and Swinnerton-Dyer conjecture, and the main ingredient of the proof is the formula of Gross and Zagier relating the heights of modularly-constructed points on E to the central derivative of L. The second prediction of BSD is a formula for the central leading term of L. This is only implied by the Gross-Zagier formula up to a nonzero rational number. One way to go on and study the BSD formula up to p-integrality is provided by a p-adic analogue of the Gross-Zagier formula due to Perrin-Riou and Kobayashi. I will explain this circle of ideas as well as its generalization to totally real fields. Time permitting, I will also discuss the representation-theoretic context.


    The talk is meant to be accessible to a broad audience.

    Updated on Sep 05, 2014 10:32 AM PDT
  71. MT Postdoc Seminar: Jet Spaces and Diophantine Geometry

    Location: MSRI: Simons Auditorium
    Speakers: Taylor Dupuy (University of New Mexico)

    We will explain how to obtain effective Mordell-Lang and Manin-Mumford using jet space techniques in the characteristic zero function field setting.

    Updated on May 16, 2014 12:58 PM PDT
  72. AT Postdoc Seminar

    Location: MSRI: Simons Auditorium
    Speakers: Joseph Hirsh (Massachusetts Institute of Technology)
    Created on Feb 07, 2014 09:37 AM PST
  73. AT Postdoc Seminar: Homotopy and arithmetic: a duality playground

    Location: MSRI: Simons Auditorium
    Speakers: Vesna Stojanoska (Massachusetts Institute of Technology)

    Homotopy theory can be thought of as the study of geometric objects and continuous deformations between them, and then iterating the idea as the deformations themselves form geometric objects. One result of this iteration is that it replaces morphism sets with topological spaces, thus remembering a lot more information. There are many examples to show that the approach of replacing sets with spaces in a meaningful way can lead to remarkable developments. In this talk, I will explain some of my recent work in the case of implementing homotopy theory in arithmetic in a way which produces new results and relationships between some classical notions of duality in both fields.

    Updated on Apr 25, 2014 11:19 AM PDT
  74. AT Postdoc Seminar: The Mirror Symmetry Conjecture and Cobordisms

    Location: MSRI: Baker Board Room
    Speakers: Hiro Tanaka (Harvard University)

    This talk--aimed for a general audience of neither topologists nor model theorists--will discuss applications of cobordisms to Kontsevich's mirror symmetry conjecture. We'll begin by stating a rough version of the
    conjecture, which builds a bridge between symplectic geometry on one hand, and on the other hand, algebraic geometry over the complex numbers. We then discuss how the theory of cobordisms, which studies when two manifolds can be the boundary of another manifold, sheds light on how to generalize the mirror symmetry conjecture, while giving us information about objects in symplectic geometry. (For example, two Lagrangians related by a compact cobordism are equivalent in the Fukaya category.)

    Updated on Apr 17, 2014 05:00 PM PDT
  75. AT Postdoc Seminar: Galois equivariance and stable motivic homotopy theory

    Location: MSRI: Simons Auditorium
    Speakers: Kyle Ormsby (MIT / Reed College)

    We will explore the relationships between Galois theory, groups acting on spaces, and motivic homotopy theory. Ultimately, for R a real closed field, we will discover that that there is a full and faithful embedding of the stable Gal(R[i]/R)-equivariant homotopy category into the stable motivic homotopy category over R.

    Updated on Mar 28, 2014 01:16 PM PDT
  76. AT Postdoc Seminar: Uses of commutative rings in homotopy theory

    Location: MSRI: Simons Auditorium
    Speakers: Sean Tilson (Universität Osnabrück)

    Homotopy theorists try to gain geometric information and insight through the use of algebraic invariants. Specifically, these invariants are useful in determining whether or not two spaces can be equivalent. We will begin with an example to demonstrate the usefulness of cohomology and some of the extra structure it possesses, such as cup products and power operations. This extra structure provides a very strong invariant of the space. As these invariants are representable functors, this extra structure is coming from the representing object. Indeed, cohomology theories possess products and power operations when they are represented by objects called commutative ring spectra. We then shift focus to studying commutative ring spectra on their own and try to detect what maps of commutative ring spectra might look like.

    Updated on Mar 28, 2014 10:11 AM PDT
  77. MT Postdoc Seminar: Strong minimality of the $j$-function

    Location: MSRI: Simons Auditorium
    Speakers: James Freitag (University of California, Berkeley)

    In this talk, we will be working in with the theory of differentially closed fields of characteristic zero; essentially this theory says that every differential equation which might have a solution in some field extension already has a solution in the differentially closed field. After introducing this theory in a bit of detail, we will sketch a proof of the strong minimality of the differential equation satisfied by the classical $j$-function starting from Pila's modular Ax-Lindemann-Weierstrass theorem. This resolves an open question about the existence of a geometrically trivial strongly minimal set which is not $\aleph _0$-categorical. If time allows, we will discuss some finiteness applications for intersections of certain sets in modular curves. This is joint work with Tom Scanlon.

    Updated on Mar 21, 2014 11:13 AM PDT
  78. MT Postdoc Seminar: Connections between Ramsey Theory and Model Theory.

    Location: MSRI: Simons Auditorium
    Speakers: Cameron Hill (Wesleyan University)

    One of the great insights of model theory is the observation that very mundane-looking "combinatorial configurations" carry a huge amount of geometric information about a structure. In this talk, I will explain what we mean by "combinatorial configuration," and then I will sketch out how configurations can be "smoothed out" to yield Ramsey classes, which can themselves be analyzed using model-theoretic tools. I will also discuss the kinds of model-theoretic dividing lines that can be defined just through the interaction of structures with Ramsey classes.

    Updated on Mar 21, 2014 11:24 AM PDT
  79. AT Postdoc Seminar: Why do algebraic topologists care about categories?

    Location: MSRI: Simons Auditorium
    Speakers: Angelica Osorno (Reed College)

    The study of category theory was started by Eilenberg and MacLane, in their effort to codify the axioms for homology. Category theory provides a language to express the different structures that we see in topology, and in most of mathematics. Categories also play another role in algebraic topology. Via the classifying space construction, topologists use categories to build spaces whose geometry encodes the algebraic structure of the category. This construction is a fruitful way of producing important examples of spaces used in algebraic topology. In this talk we will describe how this process works, starting from classic examples and ending with some recent work.

    Updated on Mar 14, 2014 10:27 AM PDT
  80. AT Postdoc Seminar: Mumford Conjecture, Characteristic Classes, Manifold Bundles, and the Tautological Ring

    Location: Space Science Lab Conference Room
    Speakers: Ilya Grigoriev (University of Chicago)

    I will describe a topologists' perspective on the history of the study of an object that Mumford called "the tautological ring" and its generalizations.

    The tautological ring was originally defined as a subring of the cohomology of the moduli space of Riemann surfaces, but can also be studied as a ring of characteristic classes of topological bundles. This point of view led to a proof of Mumford's conjecture, stating that the tautological ring coincides with the entire cohomology of the moduli space in a "stable range", as well as to some generalizations of this result. If time permits, I will explain what we know about the tautological ring outside the stable range.

    Updated on Feb 21, 2014 09:07 AM PST
  81. MT Postdoc Seminar

    Location: Space Science Lab Conference Room
    Speakers: Artem Chernikov (Institut de Mathématiques de Jussieu)
    Updated on Feb 07, 2014 03:51 PM PST
  82. AT Postdoc Seminar: Groups, Fixed Points, and Algebraic Topology

    Location: MSRI: Simons Auditorium
    Speakers: Anna Marie Bohmann (Northwestern University)

    In algebraic topology, one key way of understanding group actions on spaces is by considering families of fixed points under subgroups.  In this talk, we will discuss this basic structure and its fundamental role in understanding equivariant algebraic topology.  I will then describe some recent joint work with A. Osorno that builds on fixed point information to create equivariant cohomology theories.

    Updated on Feb 21, 2014 09:02 AM PST
  83. MT Postdoc Seminar: Finite VC-dimension in model theory and elsewhere

    Location: MSRI: Simons Auditorium
    Speakers: Pierre Simon (Centre National de la Recherche Scientifique (CNRS))

    I will present a combinatorial property---finite VC-dimension---which appeared independently in various parts of mathematics.

    In model theory it is called "NIP" and is used notably in the study of ordered and valued fields. In probability theory, it is related to "learnable classes". In combinatorics, classes of finite VC-dimension behave a lot like families of convex subsets of euclidean space. I will also talk about Banach spaces and topological dynamics.

    The talk will be accessible to postdocs of both programs.

    Updated on Feb 20, 2014 02:34 PM PST
  84. 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
  85. New computations of the Riemann zeta function

    Location: MSRI: Simons Auditorium
    Speakers: Jonathan Bober (University of Bristol)

    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.
    Updated on Aug 03, 2016 05:06 AM PDT
  86. Averages of central L-values

    Location: MSRI: Simons Auditorium
    Speakers: TBA

    Updated on Aug 03, 2016 05:05 AM PDT
  87. 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 Aug 03, 2016 05:05 AM PDT
  88. Postdoctoral Seminars FBP

    Location: MSRI: Baker Board Room

    Pizza Lunch

    Updated on Jan 24, 2011 08:17 AM PST
  89. 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
  90. 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
  91. 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
  92. E. Nordenstam's Talk

    Location: MSRI: Simons Auditorium
    Speakers: Eric Nordenstam

    Pizza Lunch

    Updated on May 13, 2013 11:01 PM PDT
  93. 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