##### Department of Mathematics,

University of California San Diego

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### Math 209 - Number Theory

## Gil Moss

#### Oklahoma State University

## A local converse theorem and the local Langlands correspondence in families

##### Abstract:

In 2012 it was conjectured by Emerton and Helm that the local Langlands correspondence for $GL(n)$ of a $p$-adic field should interpolate in $\ell$-adic families, where $\ell$ is a prime different from $p$. Recently, Helm showed that the conjecture follows from the existence of an appropriate map from the integral Bernstein center to a Galois deformation ring. In this talk we will present recent work (joint with David Helm) showing the existence of such a map and describing its image.

Host: Claus Sorensen

### April 14, 2016

### 2:00 PM

### AP&M 7321

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