##### Department of Mathematics,

University of California San Diego

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### Math 209 - Number Theory Seminar

## Niccolo Ronchetti

#### Stanford University

## A Satake homomorphism for the mod p derived Hecke algebra

##### Abstract:

Recently, Venkatesh introduced the derived Hecke algebra to explain extra endomorphisms on the cohomology of arithmetic manifolds: the crucial local construction is a derived version of the spherical Hecke algebra of a reductive p-adic group. Working with p-torsion coefficients, we will describe a Satake homomorphism for the derived spherical Hecke algebra of a p-adic group. This will allow us to understand its structure well enough to attack some global questions, which are work in progress.

Host: Claus Sorensen

### February 2, 2017

### 2:00 PM

### AP&M 7321

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