Jack Thorne (University of Cambridge)
Automorphy and potential automorphy beyond the polarizable case

Abstract: How do you prove that elliptic curves over imaginary quadratic fields are automorphic? Several years ago Frank Calegari and David Geraghty gave a generalization of the Taylor--Wiles method to this and other contexts that, assuming some conjectures about the cohomology of arithmetic locally symmetric spaces, would allow one to prove automorphy lifting theorems (the main input in the prove of automorphy of elliptic curves over Q). Recent progress in our understanding of these conjectures, due in large part to Ana Caraiani and Peter Scholze, has made it possible to prove unconditional results. I will describe a joint work in this direction with Allen, Calegari, Caraiani, Gee, Helm, Le Hung, Newton, Scholze and Taylor.