Dan Freed recently gave the Andrejewski Lectures at the Max Planck Institute for Mathematics in the Sciences in Leipzig, and has put the slides from his first lecture on-line. These give a beautiful overview of his work with Hopkins and Teleman relating loop group representations and equivariant K-theory, and explain one aspect of the relation to topological quantum field theory. His second and third lectures aren’t available on-line. The second was supposed to cover the way they use Dirac operators, which is explained in their papers. The third lecture was evidently about the relation to Chern-Simons, which isn’t in their papers so far, and which I’d be quite curious to know more about.
This fall, Dan will be giving a graduate course on Loop Groups and Algebraic Topology, which should be quite interesting.