Shimura Varieties, Local Models and Geometric Realizations of Langlands Correspondences

MEMBERS SEMINAR
Topic:Shimura Varieties, Local Models and Geometric Realizations of Langlands Correspondences
Speaker:Elena Mantovan
Affiliation:California Institute of Technology; Member, School of Mathematics
Date:Monday, November 1
Time/Room:2:00pm - 3:00pm/S-101
Video Link:https://video.ias.edu/members/mantovan

I will introduce Shimura varieties and discuss the role they play in the conjectural relashionship between Galois representations and automorphic forms. I will explain what is meant by a geometric realization of Langlands correspondences, and how the geometry of Shimura varieties and their local models conjecturally explains many aspects of these correspondences. This talk is intended as an introduction for non-number theorists to an approach to Langlands conjectures via arithmetic algebraic geometry.