Calendar

Feb
13
Tue
Number Theory Seminar: Claus Sorensen (UCSD) @ To be determined
Feb 13 @ 2:30 pm – 3:30 pm

Speaker: Claus Sorensen (UCSD)
Title: Local Langlands in rigid families
Abstract: The local Langlands correspondence attaches a representation of GL(n,F) to an n-dimensional representation of the Galois group of F (a local field). In the talk I will report on joint work with Johansson and Newton, in which we interpolate the correspondence in a family across eigenvarieties for definite unitary groups U(n). The latter are certain rigid analytic varieties parametrizing Hecke eigensystems appearing in spaces of p-adic modular forms. These varieties carry a natural coherent sheaf and we show that its dual fibers are built from the local Langlands correspondence by taking successive extensions; even at the non-classical points. Our proof employs certain elements of the Bernstein center which occur in Scholze’s trace identity. The first half of the talk is intended for a general audience with a limited background in number theory.

Feb
16
Fri
Logic seminar: David Webb
Feb 16 @ 2:30 pm – 3:30 pm

Continuing the theme of symbolic dynamics, I will demonstrate a proof of Simpson’s result that “Entropy = Dimension” for N^d and Z^d, and discuss some of Adam Day’s work generalizing these results to amenable groups.

Feb
23
Fri
Logic seminar: Umar Gaffar @ Keller 314
Feb 23 @ 2:30 pm – 3:30 pm

This week Umar Gaffar will give Shelah’s proof of the following result:

Let $\lambda$ be the cardinality of an ultraproduct of finite sets. If $\lambda$ is infinite then $\lambda=\lambda^{\aleph_0}$.

Colloquium: Rohit Nagpal (U. Chicago) @ Keller 401
Feb 23 @ 3:30 pm – 4:30 pm

Speaker: Rohit Nagpal
Title: Stability in the high dimensional cohomology of certain arithmetic groups

Abstract: Borel-Serre duality relates high dimensional cohomology of arithmetic groups to the low dimensional homology of these groups with coefficients in the Steinberg representation. We recall Bykovskii’s presentation for the Steinberg representation and explain its connection to modular symbols. Next, we describe the Steinberg representation as an object in a symmetric monoidal category, and use its presentation to describe an action of the free skew commutative algebra. Finally, we perform a Gröbner-theoretic analysis of this action to obtain new information on the homology of certain arithmetic groups with coefficients in the Steinberg representation. For example, we show that the sequence of homology groups H_1(Gamma_n(3), St_n) exhibit representation stability. This is an ongoing project with Jeremy Miller and Peter Patzt.

Mar
16
Fri
Talk Story with Thomas Hangelbroek
Mar 16 @ 3:30 pm – 4:30 pm
Mar
23
Fri
Colloquium: Christopher Marks (Cal. State Chico)
Mar 23 @ 3:30 pm – 4:30 pm
Apr
12
Thu
Undergraduate Seminar: Alex Schulte (Iowa State U.) @ Keller 402
Apr 12 @ 3:00 pm – 4:00 pm
Apr
17
Tue
Analysis Qualifying Exam
Apr 17 @ 9:00 am – 1:00 pm