Back to Departmental Colloquium: Spring 2013
Departmental Colloquium
Date: Thursday, Jan 31, 2013
Time: 4:15PM
Location: JWB 335
Peter Trapa
University of Utah
Title |
Unitary representations of reductive Lie groups |
Abstract |
Unitary representations of Lie groups appear in many places in mathematics: in harmonic analysis (as generalizations of the sines and cosines appearing in classical Fourier analysis); in number theory (as spaces of modular and automorphic forms); in quantum mechanics (as “quantizations” of classical mechanical systems); and in many other places. They have been the subject of intense study for decades, but their classification has only recently recently emerged. Perhaps surprisingly, the classification has inspired connections with interesting geometric objects (equivariant mixed Hodge modules on flag varieties). These connections have made it possible to extend the classification scheme to other related settings. The purpose of this talk is to explain a little bit about the history and motivation behind the study of unitary representations and offer a few hints about the algebraic and geometric ideas which enter into their study. This is based on a recent preprint with Adams, van Leeuwen, and Vogan. |
Number Theory
Representation Theory
Algebraic Geometry