Events for 10/15/2018 from all calendars

Geometry Seminar

Time: 3:00PM - 5:00PM

Location: BLOC 628

Speaker: Sam Raskin, UT Austin

Title: An overview of local geometric Langlands

Abstract: Abstract: The (arithmetic) Langlands program is a cornerstone of modern representation theory and number theory. It has two incarnations: local and global. The former conjectures the existence of certain "local terms," and the latter predicts remarkable interactions between these local terms. By necessity, the global story is predicated on the local. Geometric Langlands attempts to find similar patterns in the geometry of curves. However, the scope of the subject has been limited by a meager local theory, which has not been adequately developed. The subject of this talk is a part of a larger investigation into local geometric Langlands. We will give an elementary overview of the expectations of this theory, discuss a certain concrete conjecture in the area (on "temperedness"), and provide evidence for this conjecture. One application of our results is a proof of Beilinson-Bernstein localization for the affine Grassmannian for GL_2, which was previously conjectured by Frenkel-Gaitsgory. (Note: the talk will have slides. I will post the slides online before the talk, so feel free to bring a laptop if you prefer to follow along on your own computer.)

Number Theory Seminar

Time: 3:00PM - 4:00PM

Location: BLOC 624

Speaker: Matt Young, Texas A&M University

Title: The Weyl bound for Dirichlet L-functions

Abstract: The problem of estimating central values of L-functions has attracted a great deal of attention for many decades. The case of Dirichlet L-functions, which one might expect to be one of the simpler families of L-functions, has turned out to be unexpectedly difficult. In the 1960's, Burgess proved a non-trivial bound that has only been improved in some special cases. Notably, Conrey and Iwaniec obtained an improvement in the case that the Dirichlet character is real-valued. I will discuss a similar-quality improvement valid for any Dirichlet character of cube-free conductor. This is joint work with Ian Petrow.

URL: Event link

Committee P&T

Time: 4:00PM - 5:00PM

Location: BLOC 220

Description: Committee P&T Meeting