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.

number theory

Audience: researchers in the topic

UCSD number theory seminar

Series comments: Most talks are preceded by a pre-talk for graduate students and postdocs. The pre-talks start 40 minutes prior to the posted time (usually at 1:20pm Pacific) and last about 30 minutes.