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SCGP Weekly Talk: Constantin Teleman, UC Berkeley

Title: Loop groups and Matrix factorization
Speaker: Constantin Teleman, UC Berkeley
Date: Thursday, April 14, 2015
Time: 01:00pm – 02:00pm
Place: Seminar Room 313, Simons Center

 

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Abstract: Joint work with Freed and Hopkins described the K-group of the category of positive energy representations of loop groups in terms of (twisted) topological K-theory. This talk will outline a recent result (joint with Dan Freed) which refines the K-group isomorphism to an *equivalence of categories*, by tracking the circle action by loop rotation. On the category of twisted vector bundles, this action takes the form of a super-potential, and representations are identified with matrix factorizations. The construction is new even for finite-dimensional Lie groups and provides a categorification of the orbital integral character formulas (Kirillov, Harish-Chandra, I. Frenkel).