Title: Twisted K-theory, loop groups and their generalisations
Speaker: Pedram Hekmati (Adelaide)
Abstract: In recent work, Freed-Hopkins-Teleman established an isomorphism between equivariant twisted K-theory of a compact Lie group G and the representation (Verlinde) ring of the loop group LG. The latter is the gauge group of a principal G-bundle over the circle. An interesting problem is to try to generalise the circle to a higher dimensional compact manifold. This is far from obvious and some of the difficulties can be modelled in a slightly simpler setting, by replacing LG and gauge connections by objects which have only small differentiability in the Sobolev sense. In this talk, I will provide some background to this problem and discuss recent advances.