Logo

Mathematical Sciences Research Institute

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

All Colloquia & Seminars

  1. Colloquium: More products for Borcherds forms

    Location: MSRI: Simons Auditorium
    Speakers: Stephen Kudla (University of Toronto)

    In a pair of Invenitones papers in 1995 and 1998, Borcherds gave a construction of meromorphic modular forms on the hermitian symmetric domain associated to a rational quadratic space V, ( , )  of signature (n,2).  These modular forms have remarkable properties including
    (1) an explicit divisor given in terms of special divisors and
    (2) product formulas, each valid in a neighborhood of a point boundary component.
    In this lecture, after reviewing Borcherds' construction, and under the assumption that V, ( , ) admits 2-dimensional rational isotropic subspaces,  I will describe some new product formulas for these modular forms, each valid in the neighborhood of a 1-dimensional boundary component. The products involve Jacobi theta functions and eta functions.
    They should prove useful in understanding the integral theory of Borcherds forms.

    Updated on Sep 12, 2014 10:35 AM PDT
  2. Joint Seminar: Galois representation and coherent cohomology

    Location: MSRI: Simons Auditorium
    Speakers: Benoit Stroh (Centre National de la Recherche Scientifique (CNRS))

    A classical conjecture in the Langlands program asserts that coherent cohomology classes on Shimura varieties that are eigen for the action of the Hecke operators should give rise to Galois representations. For classes in H^0  it is a consequence of the p-adic interpolation by multiplication of powers of a lifting of Hasse invariant. We present here a method to tackle the case of higher cohomology groups, building on the recent work of Scholze on Shimura varieties at infinite level and the new Hasse invariants defined at this level. Joint work with Pilloni.

    Updated on Sep 25, 2014 04:23 PM PDT
  1. GRT Research Seminar: The Langlands Program and a Geometrization of Trace Formulas

    Location: MSRI: Simons Auditorium
    Speakers: Edward Frenkel (University of California, Berkeley)

    The Langlands Program relates Galois representations and automorphic representations of reductive algebraic groups defined over number fields and the fields of functions on curves over finite fields. The trace formula is a powerful tool in the study of this connection. After a brief introduction, I will outline a conjectural framework of “geometric trace formulas” in the case that the curve is defined over the complex field. It exploits a categorical formulation of the geometric Langlands correspondence. The talk is based on my joint work with Robert Langlands and Ngo Bao Chau.

    Updated on Sep 26, 2014 10:52 AM PDT
  2. Number Theory Seminar: Cycle complexity on arithmetic manifolds

    Location: 3 Evans Hall
    Speakers: Akshay Venkatesh (Stanford University)

    The topology of arithmetic hyperbolic 3-manifold is closely tied to number theory. For example, starting from an elliptic curve over Q(i), we can (conjecturally) find a "corresponding" homology class in H_2(M) where M is a finite cover of the Bianchi manifold associated to SL_2(Z[i]).

    After some motivation, I  will suggest that the topological complexity (e.g. Thurston norm) of this homology class  should be related to the arithmetic complexity (the height) of the elliptic curve.   At the end I will briefly discuss the general situation (i.e., for general arithmetic groups).

    There will be a related talk by the speaker in 740 Evans at 2:10pm to explain some background on arithmetic groups.  In particular, he will explain why number theorists are keenly interested in these groups.

    Updated on Sep 25, 2014 12:47 PM PDT
  3. NGM Research Seminar: Multiplicity one for small automorphic representations.

    Location: MSRI: Simons Auditorium
    Speakers: Gordan Savin (University of Utah)

    I will explain the Kantor-Koecher-Tits construction of almost simple algebraic groups from the Galois cohomology point of view and then, in this setting, discuss multiplicity one results for certain automorphic representations. (Joint work with Toshiyuki Kobayashi.)

    Updated on Sep 26, 2014 10:43 AM PDT
  4. NGM Research Seminar: Some simple applications of Arthur's trace formula

    Location: MSRI: Simons Auditorium
    Speakers: Erez Lapid (Weizmann Institute of Science)

    I will describe some asymptotic spectral problems in automorphic forms and the analytic and algebraic questions they spur. Joint work with Tobias Finis and Werner Müller.

    Updated on Sep 26, 2014 10:43 AM PDT
  5. 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
  6. 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
  7. Grad Student Seminar: The affine Grassmannian for GL_n

    Location: MSRI: Simons Auditorium
    Speakers: Yotam Hendel (Weizmann Institute of Science)

    We give descriptions of sheaves as functors of points and fpqc descent. We define the affine Grassmannian for GL_n, discuss gluing (the Beauville-Laszlo Theorem), and explain how the local and global versions of the affine Grassmannian for GL_n coincide.

    Updated on Sep 26, 2014 02:53 PM PDT
  8. MSRI Evans Talk: The What, Why and How of Categorification

    Location: 60 Evans Hall, UC Berkeley
    Speakers: Zsuzsanna Dancso (MSRI - Mathematical Sciences Research Institute)

    Categorification has been a central topic in the past two decades in several areas of mathematics including representation theory and low dimensional topology. In broad terms, categorification introduces richer structure by replacing algebraic structures (groups, rings, etc) by categories, in a way that lifts the important properties of the original structure.

    In this talk I will explain the general idea of categorification and illustrate it with an example from low-dimensional topology: Khovanov's link homology. We will discuss advantages and applications of categorification in different settings, and open problems in the area.

    Updated on Sep 16, 2014 10:29 AM PDT
  9. Joint Seminar

    Location: MSRI: Simons Auditorium
    Created on Sep 02, 2014 03:07 PM PDT
  10. GRT Research Seminar

    Location: MSRI: Simons Auditorium
    Created on Sep 03, 2014 11:34 AM PDT
  11. Number Theory Seminar

    Location: 740 Evans Hall
    Created on Sep 12, 2014 01:11 PM PDT
  12. NGM Research Seminar: Euler systems

    Location: MSRI: Simons Auditorium
    Speakers: David Loeffler (University of Warwick)

    The Birch--Swinnerton-Dyer conjecture is now a theorem, under some mild hypotheses, for elliptic curves over Q with analytic rank <= 1. One of the main ingredients in the proof is Kolyvagin's theory of Euler systems: compatible families of cohomology classes which can be seen as an "arithmetic avatar" of an L-function. The existence of Euler systems in other settings would have similarly strong arithmetical applications, but only a small number of examples are known.

    In this talk, I'll introduce Euler systems and their uses, and I'll describe the construction of a new Euler system, which is attached to the Rankin-Selberg convolution of two modular forms; this is joint work with Antonio Lei and Sarah Zerbes. I'll also explain recent work with Zerbes and Guido Kings where we prove an explicit reciprocity law for this Euler system, and use this to prove cases of the BSD conjecture and the finiteness of Tate-Shafarevich groups.

    Updated on Sep 23, 2014 09:30 AM PDT
  13. NGM Research Seminar: Endoscopic classification for inner forms of unitary groups

    Location: MSRI: Simons Auditorium
    Speakers: Sug Woo Shin (Massachusetts Institute of Technology)

    Arthur and Mok gave the endoscopic classification for quasi-split symplectic/orthogonal groups and quasi-split unitary groups, respectively. In this talk I explain how the results extend to inner forms of unitary groups. This is joint work with Tasho Kaletha, Alberto Minguez and Paul-James White.

    Updated on Sep 23, 2014 09:34 AM PDT
  14. NGM Pizza Seminar

    Location: MSRI: Simons Auditorium
    Updated on Sep 03, 2014 03:43 PM PDT
  15. GRT Pizza Seminar

    Location: MSRI: Simons Auditorium
    Updated on Sep 03, 2014 03:44 PM PDT
  16. Grad Student Seminar

    Location: MSRI: Simons Auditorium
    Created on Sep 03, 2014 03:23 PM PDT
  17. Colloquium

    Location: MSRI: Simons Auditorium
    Created on Sep 02, 2014 12:49 PM PDT
  18. Joint Seminar

    Location: MSRI: Simons Auditorium
    Created on Sep 02, 2014 03:24 PM PDT
  19. GRT Research Seminar

    Location: MSRI: Simons Auditorium
    Created on Sep 03, 2014 11:42 AM PDT
  20. Number Theory Seminar

    Location: 740 Evans Hall
    Created on Sep 12, 2014 01:12 PM PDT
  21. NGM Research Seminar: Paley-Wiener theorems for p-adic spherical varieties.

    Location: MSRI: Simons Auditorium
    Speakers: Yiannis Sakellaridis (Rutgers University)

    For a reductive p-adic group H, the description of the Bernstein center of the category of smooth H-representations is equivalent to the description of H x H -endomorphisms of the space of smooth, compactly supported functions on H, and the Bernstein decomposition corresponds to an H x H-equivariant decomposition of this space. The goal of this talk is to generalize this decomposition when H is replaced by a spherical variety X satisfying some strong assumptions (which cover all symmetric cases). In parallel, we will discuss the spectral transform of the space of Harish-Chandra Schwartz functions on X, generalizing Harish-Chandra's description for X=H. This is joint work with Patrick Delorme and Pascale Harinck.

    Updated on Sep 23, 2014 09:36 AM PDT
  22. NGM Research Seminar: Introductory remarks on Mochizuki's works on absolute anabelian geometry and inter-universal Teichmüller theory

    Location: MSRI: Simons Auditorium
    Speakers: Chung Pang Mok (Morningside Center of Mathematics)

    Inter-universal Teichmüller theory, as developed by Mochizuki in the past decade, is an analogue for number fields of the classical complex Teichmüller theory, and also the p-adic Teichmüller theory of Mochizuki. In this theory, the ring structure of a number field is subject to non-ring-theoretic deformation. Absolute anabelian geometry, a refinement of the anabelian geometry, plays a crucial role in inter-universal Teichmüller theory. In this talk we will try to give an introduction to these ideas, independent of their Diophantine applications.

    Updated on Sep 23, 2014 09:37 AM PDT
  23. NGM Pizza Seminar

    Location: MSRI: Simons Auditorium
    Updated on Sep 03, 2014 03:45 PM PDT
  24. GRT Pizza Seminar

    Location: MSRI: Simons Auditorium
    Updated on Sep 03, 2014 03:45 PM PDT
  25. Grad Student Seminar

    Location: MSRI: Simons Auditorium
    Created on Sep 03, 2014 03:26 PM PDT
  26. MSRI Evans Talk

    Location: 60 Evans Hall, UC Berkeley
    Speakers: Joseph Bernstein (Tel Aviv University)
    Created on Aug 08, 2014 10:01 AM PDT
  27. Joint Seminar

    Location: MSRI: Simons Auditorium
    Created on Sep 02, 2014 03:43 PM PDT
  28. GRT Research Seminar

    Location: MSRI: Simons Auditorium
    Created on Sep 03, 2014 11:48 AM PDT
  29. Number Theory Seminar

    Location: 740 Evans Hall
    Created on Sep 12, 2014 01:12 PM PDT
  30. NGM Research Seminar

    Location: MSRI: Simons Auditorium
    Created on Sep 22, 2014 11:47 AM PDT
  31. NGM Research Seminar

    Location: MSRI: Simons Auditorium
    Updated on Sep 18, 2014 02:08 PM PDT
  32. NGM Pizza Seminar

    Location: MSRI: Simons Auditorium
    Updated on Sep 03, 2014 03:46 PM PDT
  33. GRT Pizza Seminar

    Location: MSRI: Simons Auditorium
    Updated on Sep 03, 2014 03:46 PM PDT
  34. Grad Student Seminar

    Location: MSRI: Simons Auditorium
    Created on Sep 03, 2014 03:27 PM PDT
  35. MSRI Evans Talk

    Location: 60 Evans Hall, UC Berkeley
    Speakers: Atsushi Ichino (Kyoto University)
    Created on Aug 08, 2014 10:15 AM PDT
  36. Joint Seminar

    Location: MSRI: Simons Auditorium
    Created on Sep 02, 2014 04:05 PM PDT
  37. GRT Research Seminar

    Location: MSRI: Simons Auditorium
    Created on Sep 03, 2014 11:53 AM PDT
  38. Number Theory Seminar

    Location: 740 Evans Hall
    Created on Sep 12, 2014 01:13 PM PDT
  39. NGM Research Seminar

    Location: MSRI: Simons Auditorium
    Created on Sep 22, 2014 12:11 PM PDT
  40. NGM Research Seminar

    Location: MSRI: Simons Auditorium
    Updated on Sep 18, 2014 02:08 PM PDT
  41. NGM Pizza Seminar

    Location: MSRI: Simons Auditorium
    Updated on Sep 03, 2014 03:48 PM PDT
  42. GRT Pizza Seminar

    Location: MSRI: Simons Auditorium
    Updated on Sep 03, 2014 03:48 PM PDT
  43. Grad Student Seminar

    Location: MSRI: Simons Auditorium
    Created on Sep 03, 2014 03:30 PM PDT
  44. Colloquium

    Location: MSRI: Simons Auditorium
    Created on Sep 02, 2014 12:51 PM PDT
  45. Joint Seminar

    Location: MSRI: Simons Auditorium
    Created on Sep 02, 2014 04:23 PM PDT
  46. GRT Research Seminar

    Location: MSRI: Simons Auditorium
    Created on Sep 03, 2014 12:05 PM PDT
  47. Number Theory Seminar

    Location: 740 Evans Hall
    Created on Sep 12, 2014 01:14 PM PDT
  48. NGM Research Seminar

    Location: MSRI: Simons Auditorium
    Created on Sep 22, 2014 01:18 PM PDT
  49. NGM Research Seminar

    Location: MSRI: Simons Auditorium
    Updated on Sep 18, 2014 02:09 PM PDT
  50. NGM Pizza Seminar

    Location: MSRI: Simons Auditorium
    Updated on Sep 03, 2014 03:49 PM PDT
  51. GRT Pizza Seminar

    Location: MSRI: Simons Auditorium
    Updated on Sep 03, 2014 03:49 PM PDT
  52. Grad Student Seminar

    Location: MSRI: Simons Auditorium
    Created on Sep 03, 2014 03:32 PM PDT
  53. MSRI Evans Talk

    Location: 60 Evans Hall, UC Berkeley
    Speakers: Ana Caraiani (Princeton University)
    Created on Aug 08, 2014 10:40 AM PDT
  54. Joint Seminar

    Location: MSRI: Simons Auditorium
    Created on Sep 22, 2014 03:11 PM PDT
  55. GRT Research Seminar

    Location: MSRI: Simons Auditorium
    Created on Sep 03, 2014 12:12 PM PDT
  56. Number Theory Seminar

    Location: 740 Evans Hall
    Created on Sep 12, 2014 01:25 PM PDT
  57. NGM Research Seminar

    Location: MSRI: Simons Auditorium
    Created on Sep 22, 2014 01:20 PM PDT
  58. NGM Research Seminar

    Location: MSRI: Simons Auditorium
    Updated on Sep 18, 2014 02:09 PM PDT
  59. NGM Pizza Seminar

    Location: MSRI: Simons Auditorium
    Updated on Sep 03, 2014 03:51 PM PDT
  60. GRT Postdoc Seminar

    Location: MSRI: Simons Auditorium
    Created on Aug 22, 2014 03:53 PM PDT
  61. Grad Student Seminar

    Location: MSRI: Simons Auditorium
    Created on Sep 03, 2014 03:33 PM PDT
  62. Number Theory Seminar

    Location: 740 Evans Hall
    Created on Sep 12, 2014 01:26 PM PDT
  63. NGM Research Seminar

    Location: MSRI: Baker Board Room
    Created on Sep 22, 2014 01:21 PM PDT
  64. NGM Research Seminar

    Location: MSRI: Simons Auditorium
    Updated on Sep 24, 2014 03:07 PM PDT
  65. Colloquium

    Location: MSRI: Simons Auditorium
    Created on Sep 02, 2014 12:55 PM PDT
  66. Joint Seminar

    Location: MSRI: Simons Auditorium
    Created on Sep 03, 2014 09:25 AM PDT
  67. GRT Research Seminar

    Location: MSRI: Simons Auditorium
    Created on Sep 03, 2014 12:26 PM PDT
  68. Number Theory Seminar

    Location: 740 Evans Hall
    Created on Sep 12, 2014 01:29 PM PDT
  69. MSRI Evans Talk

    Location: 60 Evans Hall, UC Berkeley
    Speakers: Pierre Colmez (L'Institut de Mathématiques de Jussieu)
    Created on Aug 08, 2014 10:49 AM PDT
  70. GRT Research Seminar

    Location: MSRI: Baker Board Room
    Created on Sep 22, 2014 01:27 PM PDT
  71. Number Theory Seminar

    Location: 740 Evans Hall
    Created on Sep 12, 2014 01:31 PM PDT
  72. Colloquium

    Location: MSRI: Simons Auditorium
    Created on Sep 02, 2014 12:56 PM PDT
  73. Joint Seminar

    Location: MSRI: Simons Auditorium
    Created on Sep 03, 2014 10:27 AM PDT
  74. GRT Research Seminar

    Location: MSRI: Simons Auditorium
    Created on Sep 03, 2014 12:39 PM PDT
  75. Number Theory Seminar

    Location: 740 Evans Hall
    Created on Sep 12, 2014 01:33 PM PDT
  76. NGM Research Seminar

    Location: MSRI: Simons Auditorium
    Created on Sep 22, 2014 01:28 PM PDT
  77. NGM Research Seminar

    Location: MSRI: Simons Auditorium
    Updated on Sep 04, 2014 07:00 PM PDT
  78. NGM Pizza Seminar

    Location: MSRI: Simons Auditorium
    Updated on Sep 03, 2014 04:21 PM PDT
  79. GRT Pizza Seminar

    Location: MSRI: Simons Auditorium
    Updated on Sep 03, 2014 04:22 PM PDT
  80. Grad Student Seminar

    Location: MSRI: Simons Auditorium
    Created on Sep 04, 2014 09:50 AM PDT
  81. Colloquium

    Location: MSRI: Simons Auditorium
    Created on Sep 02, 2014 12:58 PM PDT
  82. GRT Research Seminar

    Location: MSRI: Simons Auditorium
    Created on Sep 03, 2014 12:46 PM PDT
  83. Number Theory Seminar

    Location: 740 Evans Hall
    Created on Sep 12, 2014 01:34 PM PDT

Past Seminars

seminar
  1. Seminar Grad Student Seminar

    Updated on Sep 18, 2014 10:53 AM PDT
  2. Seminar Fall 2014 5-Minute Talks

    Updated on Sep 02, 2014 08:16 PM PDT
  3. Seminar Fall 2014 5-Minute Talks

    Created on Sep 02, 2014 08:13 PM PDT
There are more then 30 past seminars. Please go to Past seminars to see all past seminars.