Noncommutative Geometry Seminar

A rigorous analytic definition of the Dirac operator
on loop spaces is a difficult open problem. When the target space
is a compact Lie group, it is possible to make sense of a Dirac
operator using methods from representation theory. In this talk,
I will briefly review this construction and its application to
twisted K-theory. I will then discuss the construction of a
universal Dirac operator, which leads to a Banach Lie group with
a highly non-trivial topology.