# From gauge theory to self-duality over Riemann surfaces II

Abstract: Last seminar I didn't get much further than recasting gauge theory in a slightly more mathematical jargon. My attempts to derive Hitchin's equations via "compactification along a Riemann surface" failed terribly due to my lack of understanding the term. I will start out with the modest goal of "dimensionally reducing" by a symmetry assumption the 4-D instanton equations on Euclidean space to equations on Euclidean 2-space, which then can be formulated coordinate independently on a Riemann surface. We then describe two incarnations of the solution space to Hitchin's equations: Higgs bundles (holomorphic view point) and complex flat bundles (topological view point) giving rise to the hyper-Kaehler structure on the moduli space. As with David's talks, the aim is to provide more of the scaffolding in a not-too-technical way to appreciate Chris Elliott’s exposition(s) on geometric Langlands and Kapustin-Witten.

Video recordings of all the seminar talks and notes (also notes from the 2020 seminar series) can be found here.

## Department of Physics