**Title: Geometric Dequantization**

**Abstract:** The well-known *orbit method* of Kirillov and Kostant produces unitary

representations of Lie groups by the *geometric quantization* construction applied

to orbits in the dual of the Lie algebra. The “trace’’ of this construction gives the

orbital integral version of character formulae. A converse *Dirac family*

construction extracts the geometric quantization data (orbit, line bundle and connection)

from each representation. Freed, Hopkins and the speaker had used this to describe the

K-group of the category of representations of loop groups of compact Lie groups in

topological terms; but a re-intepretation using the notion of *matrix factorizations*

nails the category of representations. Generalization to *real semi-simple Lie groups*

suggests a classification of tempered representations of the loop groups of the respective

loop groups.

Wednesday, May. 06, 4:30 – 5:30 p.m.

Mathematics 520

Tea will be served at 4:00 p.m.