Published on *Department of Mathematics* (https://math.yale.edu)

March 3, 2020 - 4:15pm

DL 431

Abstract: We develop the notion of a non-abelian Cauchy kernel for a framed vector bundle of rank n and degree ng on a fixed Riemann surface of genus g. This Cauchy kernel can be used to define a connection holomorphically varying in the moduli space of vector bundles. Thus we pose and answer the question regarding how the complex symplectic structure on the moduli space of Higgs bundles (or the cotangent bundle to the moduli space of vector bundles) relates to the Goldman symplectic structure. Based on work in progress with Marco Bertola and Giulio Ruzza.