Columbia Mathematics Department Colloquium

`Langlands duality, loop spaces and representations of real groups.'


David Ben-Zvi

(U. T. at Austin)

I will explain recent work with David Nadler, in which we givea new description of representations of real and complex Lie groups
in terms of coherent sheaves on complex algebraic varieties. Using the language of derived algebraic geometry, which I'll survey, we
identify coherent sheaves on the space of unparametrized loops on an algebraic variety with flat connections (D-modules) on the variety
itself.The main observation is then that some of the star playersin representation theory, in particular the Steinberg variety and the spaces
 of Langlands parameters for Harish-Chandra modules, are naturally identifiedas loop spaces. This provides a new bridge between the
 Langlands program and geometric representation theory.

February 28th, Wednesday, 5:00-6:00 pm
Mathematics 520
Tea will be served at 4:30pm