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Other Colloquia & Seminars

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  1. 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
  2. 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
  3. 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
  4. 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
  5. 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
  6. 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
  7. 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 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
  8. 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
  9. 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
  10. 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
  11. 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
  12. 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
  13. 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
  14. 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
  15. 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
  16. DMS Postdoc Seminar: Splittings, suspension flows, and polynomials for free-by-cyclic groups

    Location: MSRI: Simons Auditorium
    Speakers: Spencer Dowdall (University of Illinois at Urbana-Champaign)

    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
  17. 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
  18. 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
  19. 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
  20. 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
  21. GRT Pizza Seminar

    Location: MSRI: Simons Auditorium
    Speakers: Paul Hamacher (TU München)
    Updated on Sep 03, 2014 04:22 PM PDT
  22. 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
  23. 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
  24. 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
  25. 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
  26. 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
  27. 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
  28. 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
  29. 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
  30. 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
  31. 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
  32. GRT Pizza Seminar

    Location: MSRI: Simons Auditorium
    Updated on Sep 03, 2014 03:44 PM PDT
  33. 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
  34. 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
  35. 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
  36. GRT Pizza Seminar

    Location: MSRI: Simons Auditorium
    Updated on Sep 03, 2014 03:37 PM PDT
  37. 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
  38. 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
  39. AT Postdoc Seminar

    Location: MSRI: Simons Auditorium
    Speakers: Joseph Hirsh (Massachusetts Institute of Technology)
    Created on Feb 07, 2014 09:37 AM PST
  40. 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
  41. 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
  42. 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
  43. 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
  44. 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
  45. 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
  46. 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
  47. 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
  48. 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
  49. 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
  50. 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
  51. 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
  52. Computing critical values of quadratic Dirichlet L-functions, with an eye toward their moments.

    Location: MSRI: Simons Auditorium
    Speakers: Matthew Alderson

    Moments of L-functions has been a topic of intense research in recent years. Through the integration of random matrix theory and multiple Dirichlet series with traditional number theoretic arguments, methods for studying the moments of L-functions have been developed and, in turn, have lead to many well-posed conjectures for their behavior. In my talk, I will discuss the (integral) moments of quadratic DIrichlet L-functions evaluated at the critical point s=1/2. In particular, I will present formulas for computing the critical values for such L-functions and then compare the data for the corresponding moments to the (aforementioned) conjectured moments.
    Created on Apr 15, 2011 09:13 AM PDT
  53. 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
  54. FBP-Informal Seminar

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

    Updated on Apr 01, 2011 03:03 AM PDT
  55. Moment Polynomials for the Riemann Zeta Function

    Location: MSRI: Simons Auditorium
    Speakers: Shuntaro Yamagishi

    I will explain how we calculated the coefficients of moment
    polynomials for the Riemann zeta function for k = 4,5.., 13
    and numerically tested them against the moment polynomial conjecture.
    Updated on Mar 31, 2011 04:37 AM PDT
  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. "Computing L-functions in SAGE"

    Location: MSRI: Simons Auditorium
    Speakers: Rishikesh

    Created on Mar 23, 2011 08:26 AM PDT
  59. Postdoctoral Seminars FBP

    Location: MSRI: Baker Board Room

    Pizza Lunch

    Updated on Jan 24, 2011 08:17 AM PST
  60. 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
  61. 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
  62. 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
  63. E. Nordenstam's Talk

    Location: MSRI: Simons Auditorium
    Speakers: Eric Nordenstam

    Pizza Lunch

    Updated on May 13, 2013 11:01 PM PDT
  64. 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