Tuesday, March 3, 2020
03/03/2020 - 4:15pm
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.
03/03/2020 - 6:00pm
The classical Descartes’ theorem states that the total angular defect of a convex polyhedron is 4\pi. Such a polyhedron can be viewed as a flat surface homeomorphic to a sphere with cone singularities at vertices. We will explore the situation in both spherical geometry and hyperbolic geometry, use the Gauss-Bonnet theorem, and culminate the concept of stability.