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# Postdoc Seminars

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1. # GRT Pizza Seminar

Location: MSRI: Simons Auditorium
Updated on Sep 03, 2014 04:22 PM PDT

1. # 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
2. # 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
3. # 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
4. # 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
5. # GRT Pizza Seminar: Hitchin-Frenkel-Ngô's fibration and Vinberg semigroup

Location: MSRI: Simons Auditorium
Speakers: Alexis Bouthier (Université Paris-Sud (Orsay))

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
6. # 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
7. # NGM Pizza Seminar: Level raising mod 2 and 2-Selmer groups

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

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
8. # 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
9. # 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
10. # 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
11. # GRT Pizza Seminar

Location: MSRI: Simons Auditorium
Updated on Sep 03, 2014 03:44 PM PDT
12. # NGM Pizza Seminar: Exterior and symmetric square L-functions: compatibility with the local Langlands correspondence and a transfer between close local fields of characteristic zero and characteristic p.

Location: MSRI: Simons Auditorium
Speakers: Luis Lomeli (MSRI - Mathematical Sciences Research Institute)
Updated on Oct 02, 2014 04:55 PM PDT
13. # 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
14. # 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
15. # GRT Pizza Seminar: Steinberg Varieties and the Weyl Group: A Conceptual Approach to Springer Theory

Location: MSRI: Simons Auditorium
Speakers: Sam Gunningham (University of Texas)

I will explain how the Springer correspondence (and some generalizations) arise naturally when considering adjoint functors of parabolic induction and restriction for sheaves on a reductive group.

Updated on Sep 25, 2014 02:21 PM PDT
16. # 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
17. # GRT Pizza Seminar: Dessins D'enfant

Location: MSRI: Simons Auditorium
Speakers: Sean Rostami (University of Wisconsin)
Updated on Sep 12, 2014 10:57 AM PDT
18. # NGM Pizza Seminar: The Arthur-Selberg trace formula and the Newton stratification of Shimura varieties

Location: MSRI: Simons Auditorium
Speakers: Arno Kret (Institute for Advanced Study)
Updated on Sep 12, 2014 09:51 AM PDT
19. # GRT Pizza Seminar

Location: MSRI: Simons Auditorium
Updated on Sep 03, 2014 03:37 PM PDT
20. # 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
21. # 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
22. # AT Postdoc Seminar

Location: MSRI: Simons Auditorium
Speakers: Joseph Hirsh (Massachusetts Institute of Technology)
Created on Feb 07, 2014 09:37 AM PST
23. # 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
24. # 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
25. # 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
26. # 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
27. # 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
28. # 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
29. # 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
30. # 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
31. # 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
32. # 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
33. # 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
34. # PD Seminar: 4-stochastic measures and polyconvexity

Location: MSRI: Simons Auditorium
Speakers: Romeo Awi (Georgia Institute of Technology)

Speaker: Romeo Awi

Updated on Dec 12, 2013 01:57 PM PST
35. # 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
36. # 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
37. # 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
38. # 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
39. # PD Seminar: The Einstein-Yang-Mills phase space and the First Law of black hole mechanics

Location: 740 Evans Hall
Speakers: Stephen McCormick (University of New England)
Updated on Oct 30, 2013 03:07 PM PDT
40. # 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
41. # 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
42. # 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
43. # 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
44. # 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
45. # PD Seminar: Strict convexity properties of solutions to Monge-Ampere type equations

Location: 740 Evans Hall
Speakers: Jun Kitagawa (MSRI - Mathematical Sciences Research Institute)
Updated on Oct 10, 2013 12:57 PM PDT
46. # PD Seminar: Far from constant mean curvature solutions to the Einstein constraint equations on compact manifolds

Location: 740 Evans Hall
Speakers: Caleb Meier (University of California, San Diego)
Updated on Oct 03, 2013 11:19 AM PDT
47. # PD Seminar: Type-II singularities for Ricci flow on $R^n$

Location: 740 Evans Hall
Speakers: Haotian Wu (University of Oregon)
Updated on Sep 26, 2013 02:39 PM PDT
48. # 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
49. # 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
50. # 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
51. # 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
52. # 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
53. # 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
54. # 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.
Updated on Feb 19, 2014 08:53 AM PST
55. # 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
56. # Averages of central L-values

Location: MSRI: Simons Auditorium
Speakers: TBA

Updated on Apr 01, 2011 08:17 AM PDT
57. # 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 Jul 07, 2014 08:16 AM PDT
58. # Postdoctoral Seminars FBP

Created on Feb 18, 2011 04:31 AM PST
59. # Nonlocal equations and new notions of curvature

Location: MSRI: Baker Board Room
Speakers: Nestor Guillen

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

Location: MSRI: Baker Board Room
Speakers: Gonzalo Tornaría

Updated on Feb 13, 2011 02:59 AM PST
61. # 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
62. # "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
63. # Postdoctoral Seminars FBP

Location: MSRI: Baker Board Room

Pizza Lunch

Updated on Jan 24, 2011 08:17 AM PST
64. # Postdoctoral and Graduate Student Seminar TBA

Location: MSRI: Simons Auditorium

Pizza Lunch

Updated on May 13, 2013 11:01 PM PDT
65. # Gluing semiclassical resolvent estimates via propagation of singularities.

Location: MSRI: Baker Board Room
Speakers: Kiril Datchev

Pizza Lunch

Updated on Aug 14, 2014 02:45 PM PDT
66. # Lower bounds for the volume of the nodal sets

Location: MSRI: Simons Auditorium
Speakers: Hamid Hezari

Pizza Lunch

Updated on Dec 19, 2013 01:12 PM PST
67. # 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
68. # Harmonic maps into conic surfaces with cone angles less than $2\pi$

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

Speakers: Benjamin Young

Updated on May 29, 2013 09:25 AM PDT
70. # Postdoctoral and Graduate Student Seminar TBA

Location: MSRI: Baker Board Room

Pizza Lunch

Updated on May 13, 2013 11:01 PM PDT
71. # Dihedral symmetry and the Razumov-Stroganov Ex-Conjecture

Location: MSRI: Baker Board Room

Pizza Lunch

Updated on Nov 05, 2010 07:12 AM PDT
72. # 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
73. # "Edge scaling limits for non-Hermitian random matrices"

Location: MSRI: Simons Auditorium
Speakers: Martin Bender

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

Location: MSRI: Simons Auditorium

Pizza Lunch

Updated on May 13, 2013 11:01 PM PDT
75. # From Oscillatory Integrals to a Cubic Random Matrix Model"

Speakers: Alfredo Deaño

Pizza Lunch

Updated on Oct 23, 2010 05:07 AM PDT
76. # 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
77. # 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
78. # 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
79. # 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
80. # 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
81. # E. Nordenstam's Talk

Location: MSRI: Simons Auditorium
Speakers: Eric Nordenstam

Pizza Lunch

Updated on May 13, 2013 11:01 PM PDT
82. # 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