The Hitchin connection for the Quantization of the moduli space of parabolic bundles on surfaces with marked points
The subject of my studies for the last five years as a PhD student at QGM, has been the moduli space of flat connections over a surface with punctures, each assigned with a weight. We define different moduli spaces, using Sobolev spaces and parabolic bundles, that are diffeomorphic on the smooth locus to the moduli space of flat connections. The aim of the thesis is to find a Hitchin connection in this setting, with specific constraints on the weights and the genus of the surface. We use the construction of the Hitchin connection with metaplectic correction by Andersen, Gammelgaard and Roed, to construct such a projectively flat Hitchin connection on the moduli space of parabolic bundles.
Thesis advisor: Jørgen Ellegaard Andersen