Back to Departmental Colloquium: Spring 2023
Departmental Colloquium
Date: Thursday, Mar 30, 2023
Time: 4:00PM - 5:00PM
Location: JWB 335
Manish Patnaik
University of Alberta
Title |
Automorphic Forms on Loop Groups |
Abstract |
The loop group, or the space of maps from the circle into a Lie group G, is one of the most tractable examples of an infinite-dimensional group of continuous symmetries. After reviewing some basic facts about such loop groups (and their central extensions), we shall focus on their arithmetic theory in order to describe certain automorphic forms that live on them. It has long been expected that a comparison of automorphic forms between G and the loop group of G should provide a new tool to study automorphic L-functions attached to G. We will describe recent progress in this direction by A. Braverman-D. Kazhdan and by S.D. Miller, H. Garland, and the speaker, focusing especially on how the theory of Eisenstein series on loop groups bifurcates into ‘positive’ and ’negative’ directions, distinctions which we note are invisible from the finite-dimensional theory. Joint with with Stephen D. Miller and Howard Garland. |
Number Theory