Constructing solutions of Hitchin's equations near the ends of the moduli space

Abstract: Hitchin’s equations are a system of gauge theoretic equations on a Riemann surface that are of interest in many areas including representation theory, Teichmuller theory, and the geometric Langlands correspondence. In this talk, I’ll describe what solutions of SL(n,C)-Hitchin’s equations ``near the ends’’ of the moduli space look like. This construction generalizes Mazzeo-Swoboda-Weiss-Witt’s (2014) construction of SL(2,C)-solutions of Hitchin’s equations where the Higgs field is “simple.” This is ongoing work.