Ana Caraiani will speak on

Galois representations and torsion classes

Abstract: I will describe joint work in progress with Allen, Calegari, Gee, Helm, Le Hung, Newton, Scholze, Taylor, and Thorne on potential modularity for elliptic curves over imaginary quadratic fields. The key ingredients are the Calegari-Geraghty method, a result on torsion in the cohomology of Shimura varieties that is joint with Scholze, and a new argument for Ihara avoidance in proving modularity lifting theorems. I will try to explain these ingredients in my talk.