##### Department of Mathematics,

University of California San Diego

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### Math 209 - Number Theory Seminar

## Jize Yu

#### California Institute of Technology

## The integral geometric Satake equivalence in mixed characteristic

##### Abstract:

The integral geometric Satake equivalence in mixed characteristic Abstract: The geometric Satake equivalence establishes a link between two monoidal categories: the category of perverse sheaves on the local Hecke stack and the category of finitely generated representations of the Langlands dual group. It has many important applications in the study of the geometric Langlands program and number theory. In this talk, I will discuss the integral coefficient geometric Satake equivalence in the mixed characteristic setting. It generalizes the previous results of Lusztig, Ginzburg, Mirkovic-Vilonen, and Zhu. Time permitting, I will discuss an application of this result in constructing a Jacquet-Langlands transfer.

Host: Kiran Kedlaya

### April 30, 2020

### 2:00 PM

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