Title: Analytic Aspects of Automorphic L-functions
Speaker: Wenzhi Luo
Abstract: The theory of automorphic forms and the associated L-functions has rich history, pioneered by Dirichlet, Eisenstein, Klein, Poincaré , Hecke and Artin, among others. It lies at the crossroads of Number Theory, Harmonic Analysis on Locally Symmetric Spaces, Representation Theory of Algebraic Groups, and Arithmetic Geometry, and plays a central role as the building block in the far-reaching Langlands program on Functoriality Conjecture and Non-Abelian Reciprocity Law.
In this lecture, I will attempt to provide a glimpse into the fascinating area of automorphic L-functions, focusing on their analytic aspects and general perspectives, and highlighting some of the intriguing problems with the approaches via the spectral theory of hyperbolic Laplacian and the trace formulas.