##### Department of Mathematics,

University of California San Diego

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### Math 209: Number Theory Seminar

## Christian Klevdal

#### UC San Diego

## Local systems on Shimura varieties

##### Abstract:

A large area of modern number theory (the Langlands program) studies a deep correspondence between the representation theory of Galois groups, algebraic varieties and certain analytic objects (automorphic forms). Many spectacular theorems have come from this area, for example the key insight in Wiles' proof of Fermat's last theorem was a connection between elliptic curves, modular forms and Galois representations.

The goal of this talk is to explain how geometric constructions, particularly related to Shimura varieties, arise naturally in the Langlands program. I will then talk about joint work with Stefan Patrikis, stating that Galois representations arising from certain Shimura varieties satisfy the properties predicted by the correspondence introduced above.

### May 23, 2024

### 2:00 PM

APM 6402 and online (see https://www.math.ucsd.edu/~nts

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