Atiyah-Segal-Singer equivariant index theorem for the Hitchin moduli space

Yang-Mills theory on Riemann surfaces is not only a mathematically well defined example of quantum field theory, but is in fact an exactly solvable one.  After a broad survey of the theory and its (exactly solvable) deformations we will focus our attention on the "complexification" of this beautiful story. In particular, we will construct new topological field theories (TFTs) whose partition functions compute the equivariant volume of the Hitchin moduli space and the equivariant version of the Verlinde formula. The latter can be thought of as the character of the infinite-dimensional Hilbert space in Chern-Simons theory with complex gauge group.