Title: Bounds on automorphic periods and L-functions  and representation theory.
Abstract. Bounds on periods of automorphic functions is a central topic in Number Theory since foundational works of Jacobi and Ramanujan.  I will discuss an approach based on representation theory methods which was developed during past 20 years. Recently this approach allowed P. Nelson and A. Venkatesh obtain new remarkable result in this classical area. Towards the end of my lecture, I will briefly discuss this new development which is based on the Orbit Method of A. Kirillov.
Livestream/Recording Link: https://huji.cloud.panopto.eu/Panopto/Pages/Viewer.aspx?id=2f4eaf56-f258...