##### Department of Mathematics,

University of California San Diego

****************************

### Number Theory Seminar

## Michael Skirvin

#### Northwestern University

## Geometric Langlands and global Springer theory

##### Abstract:

\indent I will begin by giving a broad overview of the geometric Langlands progam, with emphasis on the local to global results of Beilinson, Drinfeld, Frenkel, and Gaitsgory. Their methods are particularly compelling because they do not have analogues in the original Langlands program. Using geometric Langlands as motivation, I will introduce the Hitchin fibration and describe recent results regarding the geometry of the global nilpotent cone (i.e., Hitchin fiber over zero). These results may be viewed in the context of a global analogue of Springer theory, which suggests many future directions. If there is time, I will also explain relations to classical and higher rank Brill-Noether theory.

Host: Cristian Popescu

### October 27, 2011

### 2:00 PM

### AP&M 7321

****************************