Title: Gauge Theory and Hyper-Kähler Reduction
Speaker: Jaime Mendizabal
Abstract: Given a hyper-Kähler manifold with a tri-holomorphic action of some Lie group, it is sometimes possible to build a moment map which allows a quotient construction to be carried out, analogous to the cases of symplectic and Kähler reduction. As it turns out, in gauge theory some moduli space constructions can be viewed as an infinite-dimensional hyper-Kähler reduction. This is done by considering the action of the gauge group on a certain configuration space (for example, a space of connections on a bundle). Under appropriate conditions, we have a moment map that corresponds to an equation that we want to solve. The construction of the moduli space of solutions to this equation, modulo gauge transformations, can then be considered as an infinite-dimensional hyper-Kähler reduction, with the finite-dimensional quotient carrying a hyper-Kähler metric. In this talk, we will introduce hyper-Kähler reduction, gauge theory, and some of the problems that relate the two.
Some snacks will be provided before and after the talk.