
DMS Postdoc Seminar: An Overview of the Nahm Transform
Location: MSRI: Simons Auditorium Speakers: Andres LarrainHubach (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 YangMills 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 
GAAHD Postdoc Seminar: Hausdorff dimension of product sets
Location: MSRI: Simons Auditorium Speakers: Nicolas de Saxce (Université de Paris XIII (ParisNord))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 
DMS Postdoc Seminar
Location: MSRI: Simons Auditorium Speakers: Guillaume Dreyer (University of Notre Dame), Nicolas de Saxce (Université de Paris XIII (ParisNord))Created on Jan 28, 2015 02:04 PM PST 
GAAHD Postdoc Seminar
Location: MSRI: Simons Auditorium Speakers: Guillaume Dreyer (University of Notre Dame), Nicolas de Saxce (Université de Paris XIII (ParisNord))Created on Jan 28, 2015 02:05 PM PST 
DMS Postdoc Seminar
Location: MSRI: Simons Auditorium Speakers: Guillaume Dreyer (University of Notre Dame), Nicolas de Saxce (Université de Paris XIII (ParisNord))Created on Jan 28, 2015 02:06 PM PST 
GAAHD Postdoc Seminar
Location: MSRI: Simons Auditorium Speakers: Guillaume Dreyer (University of Notre Dame), Nicolas de Saxce (Université de Paris XIII (ParisNord))Created on Jan 28, 2015 02:07 PM PST
Past Postdoc

GAAHD Postdoc Seminar: Small generators of integral orthogonal groups
Location: MSRI: Simons Auditorium Speakers: Han Li (University of Texas)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 
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 FockGoncharov'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 
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 (Yale University)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 BowenMargulis measure on its boundary with the PattersonSullivan 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 
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 
GAAHD Postdoc Seminar: Gap distributions for saddle connections on the octagon
Location: MSRI: Simons Auditorium Speakers: Grace Work (University of Illinois at UrbanaChampaign)(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 
DMS Postdoc Seminar: Andreev's theorem on projective Coxeter polyhedra
Location: MSRI: Simons Auditorium Speakers: GyeSeon Lee (RuprechtKarlsUniversität Heidelberg)In 1970, E.M. Andreev gave a full description of 3dimensional 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 subgeometry 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 
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 nonuniform 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 
DMS Postdoc Seminar: Degeneration of complex projective structures on surfaces that converges in the character variety
Location: MSRI: Baker Board Room Speakers: Shinpei Baba (RuprechtKarlsUniversität 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 ``neckpinching'’ type degeneration of complex projective structures when their holonomy representations converge in the character variety.Created on Mar 05, 2015 04:20 PM PST 
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 (Yale University)In this talk, we will study the behavior of trajectories of diagonal geodesic flow on product space of copies of dimensional noncompact hyperbolic spaces with finite volume, and shall show that the Hausdorff dimension of the collection of divergent trajectories is equal to . This extends a result of Yitwah Cheung.Updated on Feb 27, 2015 12:18 PM PST 
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 fourholed sphere S, and of the threeholed 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 
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 BourgainLindenstraussMichelVenkatesh. Updated on Feb 20, 2015 09:13 AM PST 
DMS Postdoc Seminar: Splittings, suspension flows, and polynomials for freebycyclic groups
Location: MSRI: Simons Auditorium Speakers: Spencer Dowdall (University of Illinois at UrbanaChampaign)The semidirect product of a finiterank 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 semiflows 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 
GAAHD Postdoc Seminar: Pointwise equidistribution for oneparameter 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 oneparametr 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 BorelCantelli lemma.Updated on Feb 13, 2015 11:12 AM PST 
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 
GAAHD Postdoc Seminar: AlmostFuchsian space and entropy of minimal surfaces
Location: MSRI: Simons Auditorium Speakers: Andrew Sanders (University of Illinois at Chicago)An almostFuchsian manifold is a quasiFuchsian 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 almostFuchsian 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 quasiFuchsian groups.
Updated on Feb 05, 2015 11:45 AM PST 
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 
GRT Pizza Seminar
Location: MSRI: Simons Auditorium Speakers: Paul Hamacher (TU München)Updated on Sep 03, 2014 04:22 PM PDT 
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 RodriguezVillegas 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 
NGM Pizza Seminar: Hyperelliptic curves, local character expansions, and endoscopy
Location: MSRI: Simons Auditorium Speakers: ChengChiang Tsai (Harvard University)A representation of a reductive padic group has its character as a distribution on the group. Its asymptotic behavior near the identity is given by a finiteterm local character expansion of HarishChandra. 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 BhargavaGross on arithmetic invariant theory of $SO_{2n+1}$ on $\text{Sym}^2$.
Updated on Nov 04, 2014 04:18 PM PST 
GRT Pizza Seminar: The geometry of Gbundles 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 Gbundles 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 
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 ColemanMazur 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 
GRT Pizza Seminar: HitchinFrenkelNgô'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 
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_peigenform of weight k>1 such that the valuation of its U_peigenvalue is <k1, 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 higherdimensional Shimura varieties. Part of this is joint work with Vincent Pilloni.
Updated on Oct 23, 2014 09:18 AM PDT 
NGM Pizza Seminar: Level raising mod 2 and 2Selmer 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 2Selmer groups of modular forms in level raising families.
This is joint work with Chao Li.
Updated on Oct 23, 2014 09:15 AM PDT 
GRT Pizza Seminar: BeilinsonDrinfeld's construction of automorphic Dmodules
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 
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) KnizhnikZamolodchikov 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 
NGM Pizza Seminar: Generic smoothness for Gvalued potentially semistable deformation rings
Location: MSRI: Simons Auditorium Speakers: Rebecca BellovinKisin showed that the generic fibers of potentially semistable (framed) deformation rings of padic 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 
GRT Pizza Seminar
Location: MSRI: Simons AuditoriumUpdated on Sep 03, 2014 03:44 PM PDT 
NGM Pizza Seminar: Exterior and symmetric square Lfunctions: 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 
GRT Pizza Seminar: Flying rings and the KashiwaraVergne problem
Location: MSRI: Simons Auditorium Speakers: Zsuzsanna Dancso (MSRI  Mathematical Sciences Research Institute)I will present a sketch of a topological proof of the KashiwaraVergne 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 
NGM Pizza Seminar: Weyl's law for automorphic forms and Hecke operators
Location: MSRI: Simons Auditorium Speakers: Jasmin Matz (Rheinische FriedrichWilhelmsUniversität 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, LindenstraussVenkatesh). 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 Lfunctions. 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 
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 
NGM Pizza Seminar: Description of the Moduli Space for U(n,0) as a Tensor Product of Categories.
Location: MSRI: Simons Auditorium Speakers: Zavosh AmirKhosravi (Fields Institute for Research in Mathematical Sciences)Shimura varieties attached to unitary groups of signature (nr,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 rankn positivedefinite hermitian modules.
Updated on Sep 19, 2014 10:04 AM PDT 
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 
NGM Pizza Seminar: The ArthurSelberg 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 
GRT Pizza Seminar
Location: MSRI: Simons AuditoriumUpdated on Sep 03, 2014 03:37 PM PDT 
NGM Pizza Seminar: The padic GrossZagier formula on Shimura curves.
Location: MSRI: Simons Auditorium Speakers: Daniel Disegni (McGill University)For elliptic curves E/Q whose Lfunction 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 SwinnertonDyer conjecture, and the main ingredient of the proof is the formula of Gross and Zagier relating the heights of modularlyconstructed 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 GrossZagier formula up to a nonzero rational number. One way to go on and study the BSD formula up to pintegrality is provided by a padic analogue of the GrossZagier formula due to PerrinRiou 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 representationtheoretic context.
The talk is meant to be accessible to a broad audience.
Updated on Sep 05, 2014 10:32 AM PDT 
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 MordellLang and ManinMumford using jet space techniques in the characteristic zero function field setting.
Updated on May 16, 2014 12:58 PM PDT 
AT Postdoc Seminar
Location: MSRI: Simons Auditorium Speakers: Joseph Hirsh (Massachusetts Institute of Technology)Created on Feb 07, 2014 09:37 AM PST 
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 
AT Postdoc Seminar: The Mirror Symmetry Conjecture and Cobordisms
Location: MSRI: Baker Board Room Speakers: Hiro Tanaka (Harvard University)This talkaimed for a general audience of neither topologists nor model theoristswill 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 
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 
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 
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 AxLindemannWeierstrass 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 
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 mundanelooking "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 modeltheoretic tools. I will also discuss the kinds of modeltheoretic dividing lines that can be defined just through the interaction of structures with Ramsey classes.
Updated on Mar 21, 2014 11:24 AM PDT 
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 
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 
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 
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 
MT Postdoc Seminar: Finite VCdimension in model theory and elsewhere
Location: MSRI: Simons Auditorium Speakers: Pierre Simon (Centre National de la Recherche Scientifique (CNRS))I will present a combinatorial propertyfinite VCdimensionwhich 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 VCdimension 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 
PD Seminar: 4stochastic 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 
PD Seminar: Regularity of shadows and the singular set associated to a MongeAmpere equation
Location: 740 Evans Hall Speakers: Emanuel Indrei (Carnegie Mellon University)Updated on Nov 15, 2013 09:42 AM PST 
PD Seminar: The spherically symmetric SU(2) EinsteinYangMills equations
Location: 740 Evans Hall Speakers: Daniel Jackson (Monash University)Updated on Nov 15, 2013 09:41 AM PST 
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 
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 
PD Seminar: The EinsteinYangMills 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 
PD Seminar: Adding a vanishing Dirichlet energy to the Monge cost: some surprising effects
Location: 740 Evans Hall Speakers: Jean Louet (Université de Paris XI)Updated on Oct 30, 2013 03:07 PM PDT 
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 
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 
PD Seminar: Linear waves on Kerrde Sitter cosmologies
Location: 740 Evans Hall Speakers: Volker Schlue (University of Toronto)Updated on Oct 17, 2013 11:27 AM PDT 
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 
PD Seminar: Strict convexity properties of solutions to MongeAmpere type equations
Location: 740 Evans Hall Speakers: Jun Kitagawa (MSRI  Mathematical Sciences Research Institute)Updated on Oct 10, 2013 12:57 PM PDT 
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 
PD Seminar: TypeII 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 
PD Seminar: Noncollision singularities in the Newtonian Nbody problem
Location: 740 Evans Hall Speakers: Jinxin Xue (University of Chicago)Updated on Sep 26, 2013 02:38 PM PDT 
PD Seminar: Bochner inequality and the entropic curvature dimension condition for metric measure spaces.
Location: 740 Evans Hall Speakers: Matthias Erbar (Rheinische FriedrichWilhelmsUniversität Bonn)Updated on Sep 26, 2013 09:02 AM PDT 
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 
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 
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 
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 CWcomplexes.
Updated on May 10, 2013 10:59 AM PDT 
New computations of the Riemann zeta function
Location: MSRI: Simons Auditorium Speakers: Jonathan BoberI'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 
Review and recent works on the large time asymptotics for HamiltonJacobi equations
Location: MSRI: Baker Board Room Speakers: Hiroyoshi MITAKECreated on Apr 08, 2011 06:19 AM PDT 
Averages of central Lvalues
Location: MSRI: Simons Auditorium Speakers: TBAUpdated on Apr 01, 2011 08:17 AM PDT 
NonDegeneracy of an EllipticFree 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 nondegeneracy of the
largest subsolution near the free boundary.Updated on Jul 07, 2014 08:16 AM PDT 
Postdoctoral Seminars FBP
Created on Feb 18, 2011 04:31 AM PST 
Nonlocal equations and new notions of curvature
Location: MSRI: Baker Board Room Speakers: Nestor Guillen
Updated on Feb 13, 2011 03:00 AM PST 
Brandt module of ternary quadratic forms
Location: MSRI: Baker Board Room Speakers: Gonzalo Tornaría
Updated on Feb 13, 2011 02:59 AM PST 
Regularity for Elliptic Equations with Discontinous BMO Coefficients in Reifenberg Flat Domains
Location: MSRI: Simons AuditoriumPizza Lunch
Updated on Feb 04, 2011 05:25 AM PST 
"Lowlying zeros of Dedekind zeta functions"
Location: MSRI: Simons Auditorium Speakers: Andrew YangPizza Lunch
Updated on Feb 04, 2011 05:52 AM PST 
Postdoctoral Seminars FBP
Location: MSRI: Baker Board RoomPizza Lunch
Updated on Jan 24, 2011 08:17 AM PST 
Postdoctoral and Graduate Student Seminar TBA
Location: MSRI: Simons AuditoriumPizza Lunch
Updated on May 13, 2013 11:01 PM PDT 
Gluing semiclassical resolvent estimates via propagation of singularities.
Location: MSRI: Baker Board Room Speakers: Kiril DatchevPizza Lunch
Updated on Aug 14, 2014 02:45 PM PDT 
Lower bounds for the volume of the nodal sets
Location: MSRI: Simons Auditorium Speakers: Hamid HezariPizza Lunch
Updated on Dec 19, 2013 01:12 PM PST 
Nonintersecting Brownian Motions at a Tacnode: Soft and Hard Edge Case.
Location: MSRI: Simons AuditoriumPizza Lunch
Updated on Nov 29, 2010 03:22 AM PST 
Harmonic maps into conic surfaces with cone angles less than $2\pi$
Updated on Nov 22, 2010 03:33 AM PST 
A tale of two tiling problems
Speakers: Benjamin Young
Updated on May 29, 2013 09:25 AM PDT 
Postdoctoral and Graduate Student Seminar TBA
Location: MSRI: Baker Board RoomPizza Lunch
Updated on May 13, 2013 11:01 PM PDT 
Dihedral symmetry and the RazumovStroganov ExConjecture
Location: MSRI: Baker Board RoomPizza Lunch
Updated on Nov 05, 2010 07:12 AM PDT 
Geometric structures in the study of the geodesic ray transform
Location: MSRI: Simons Auditorium Speakers: JuhaMatti PerkkioPizza Lunch
Updated on Oct 29, 2010 06:27 AM PDT 
"Edge scaling limits for nonHermitian random matrices"
Location: MSRI: Simons Auditorium Speakers: Martin Bender
Updated on Oct 29, 2010 07:57 AM PDT 
Postdoctoral and Graduate Student Seminar TBA
Location: MSRI: Simons AuditoriumPizza Lunch
Updated on May 13, 2013 11:01 PM PDT 
From Oscillatory Integrals to a Cubic Random Matrix Model"
Speakers: Alfredo DeañoPizza Lunch
Updated on Oct 23, 2010 05:07 AM PDT 
Application of RiemannHilbert Problems in Modelling of Cavitating Flow
Location: MSRI: Simons Auditorium Speakers: Anna ZemlyanovaPizza Lunch
Updated on Oct 18, 2010 02:57 AM PDT 
Albrecht Durer, Magic Squares, and Unitary Matrix Integrals
Location: MSRI: Simons Auditorium Speakers: Jonathan NovakPizza Lunch
Updated on Dec 04, 2013 12:45 PM PST 
Imaging Edges in Random Media
Location: MSRI: Simons Auditorium Speakers: Fernando Guevara VasquezPizza 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 
Integrable Equations for Random Matrix Spectral Gap Probabilities
Location: MSRI: Simons Auditorium Speakers: Igor RumanovPizza Lunch
Connections are exposed between integrable equations for spectral gap probabilities of unitary invariant ensembles of random matrices (UE) derived by different  TracyWidom (TW) and AdlerShiotavan 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 threeterm recurrence for orthogonal polynomials (OP) and onedimensional Toda lattice (or TodaAKNS) integrable hierarchy whose flows are the continuous transformations between different OP bases. Similar connections exist for coupled UE. The gap probabilities for onematrix 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 twomatrix coupled GUE are found.Updated on May 13, 2013 11:01 PM PDT 
The Inverse Calderon Problem for Schrödinger Operator on Riemann Surfaces
Location: MSRI: Simons Auditorium Speakers: Leo tzouPizza 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. DMS0807502 during this work.Updated on May 13, 2013 11:01 PM PDT 
E. Nordenstam's Talk
Location: MSRI: Simons Auditorium Speakers: Eric NordenstamPizza Lunch
Updated on May 13, 2013 11:01 PM PDT 
Resistor Networks and Optimal Grids for Electrical Impedance Tomography with Partial Boundary Measurements
Location: MSRI: Baker Board Room Speakers: Alexander MamonovPizza 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 nonlinear inverse problem is known to be exponentially illconditioned. 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 optimizationbased 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 linearizationbased inversion methods.Updated on May 13, 2013 11:01 PM PDT