EVENT DETAILS AND ABSTRACT

Title: Sup-norms of automorphic forms
Speaker: Nicolas Templier
Speaker Info: Princeton
Brief Description:
Special Note:
Abstract:

If f is a cuspidal automorphic forms on a reductive group G it is classical to study its value distribution and in particular its sup-norm, that is the maximum of |f(g)|. We will survey recent results on the problem of bounding the sup-norm, focusing on the GL(2) case which includes Hecke--Maass cusp forms, holomorphic and Hilbert modular forms and automorphic forms on quaternion algebras. There are interesting connections with local harmonic analysis (archimedean and non-archimedean), quantum chaos, integers represented by quadratic forms. Then we will explain an approach to lower bounds via unipotent periods with a new formula for non-archimedean Whittaker functions.