### Unitary representations of reductive Lie groups

- Series
- School of Mathematics Colloquium
- Time
- Thursday, March 3, 2016 - 16:05 for 1 hour (actually 50 minutes)
- Location
- Skiles 005
- Speaker
- Peter Trapa – University of Utah

Unitary representations of Lie groups appear in many guises in
mathematics: in harmonic analysis (as generalizations of 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 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 joint work with Adams, van Leeuwen,
and Vogan.