Applications (Part Two)
David Ben-Zvi (The University of Texas at Austin)
April 14th, 2007 at University of Oxford
Special thanks to Charles Beesley, Head of Media Production, University of Oxford
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Abstract:
In the final unit we will explain some applications of the geometric Langlands program to representation theory. We will begin with a crash course in geometric representation theory, focussing on the Beilinson-Bernstein localization and the appearance of braid group actions. Next we'll outline Bezrukavnikov's geometric theory of affine Hecke algebras (the "tamely ramified" geometric Langlands program), a new fundamental tool in representation theory with wide-ranging implications. Finally we'll see how geometric Langlands can be applied to provide a new approach to the representation theory of real Lie groups (joint work with David Nadler).