The Ruth Moufang Lectures will have their fourth iteration on March 21st and 22nd, 2024 in Frankfurt am Main. We are happy to announce that our speaker will be Ana Caraiani.

Ana Caraiani (Imperial College London) – Colloquium “Elliptic curves and modularity”

Abstract: The goal of this talk is to give you a glimpse of the Langlands program, a central topic at the intersection of algebraic number theory, algebraic geometry and representation theory. I will focus on a celebrated instance of the Langlands correspondence, namely the modularity of elliptic curves. In the first part of the talk, I will give an explicit example, discuss the different meanings of modularity for rational elliptic curves, and mention applications. In the second part of the talk, I will discuss what is known about the modularity of elliptic curves over more general number fields.