Seminars & Colloquia Calendar

Abstract: Classical Teichmuller space encodes complex structures on a closed oriented surface but may also be identified with the space of hyperbolic structures or as a distinguished component in the \(PSL(2,\R)\)-character variety for the surface. These different perspectives lead to interesting generalizations known as higher Teichmuller spaces.  Higgs bundles on Riemann surfaces are holomorphic bundles with an auxiliary feature known as the Higgs field. With roots in physical and mathematical gauge theory they have moduli spaces with rich algebraic and geometric structure.  We will give a bird's eye view of these two seemingly distinct topics and describe some of the sometimes surprising ways they interact.