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.

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