Program The workshop will constitute a weeklong retreat with talks and organized discussions during the mornings and evenings; the afternoon schedule will be kept clear for informal discussions and collaborations. The workshop will generally focus on understanding the relationship between the representation theory of a loop group LG and the equivariant twisted K-theory of G. Specifically, talks will develop the geometric approach to the representation theory of loop groups, K-theory and its twisted variant, basic computations of K-theory, Dirac operators and the families index theorem, extended topological field theories and Chern-Simons theory, conformal field theory and the WZW model, and recent work on extending Chern-Simons and gauged Gromov-Witten theory.