Jacob Lurie, Harvard University
Abstract: Let G be a finite group. One of the main theorems of representation theory asserts that the construction which assigns to each representation of G its character induces an isomorphism between the representation ring of G and the ring of conjugation-invariant functions on G.

This isomorphism can be interpreted as giving a concrete description of the G-equivariant K-theory of a point "with complex coefficients". Hopkins, Kuhn, and Ravenel developed an analogous "character theory" for a large class of cohomology theories, known as Morava E-theories.

In this talk, I'll review the work of Hopkins-Kuhn-Ravenel, describe an extension of it, and indicate briefly how this extension can be used to produce examples of topological quantum field theories.