##### Department of Mathematics,

University of California San Diego

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### Math 295 - Mathematics Colloquium

## Claus Sorensen

#### UCSD

## A gentle introduction to local Langlands in families

##### Abstract:

This talk will be geared towards a general audience. Assuming only familiarity with p-adic numbers, we will first discuss the local Langlands correspondence for GL(n), and explain why it's a wide-ranging generalization of local class field theory. Then we will follow Emerton and Helm in trying to extrapolate it to a correspondence between representations over more general local rings -- whereupon we reformulate the conjectural Ihara lemma in this language. The latter is a big open problem for n>2, which occurred in work of Clozel, Harris, and Taylor, in their attempt to mimic the proof of Fermat's Last Theorem in the context of GL(n).

Host: Peter Ebenfelt

### February 13, 2014

### 3:00 PM

### AP&M 6402

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