Characters tell all: Harmonic analysis on reductive, p-adic groups | Department of Mathematics

Characters tell all: Harmonic analysis on reductive, p-adic groups

Event Information
Event Location: 
GAB 406, 4-5 PM; Refreshments: GAB 472, 3:30 PM
Event Date: 
Monday, October 25, 2010 - 4:00pm

It has been said that the 'proper' realisation of a group always involves its action by symmetries on some space. This principle manifests everywhere from geometry, to classical analysis, to number theory. Unfortunately, most symmetries are too hard to study directly, so we must usually linearise them. The study of linearised group actions is called representation theory. In the late 1960's and early 1970's, Langlands proposed a far-reaching collection of conjectures unifying algebraic, geometric, and analytic perspectives on representation theory. Much deep work has been done in the pursuit of these conjectures, but, until recently, the fundamental objects of harmonic analysis, group characters, have not been put to their full use. In this talk, we will discuss the application of character formulas to questions about stable distributions on reductive, $p$-adic groups.