Geometry/Topology Seminar
Tuesday March 9th, 2021
Time: 4:30 PM - 5:30 PM
Title: Higgs bundles and higher Teichmuller spaces
Speaker: Oscar Garcia-Prada, Institute of Mathematical Sciences (ICMAT, Madrid)
Location: Online
Abstract:
It is well-known that the Teichmuller space of a compact surface can be identified with a connected component of the moduli space of representations of the fundamental group of the surface in PSL(2,R). Higher Teichmueller spaces are generalizations of this, where PSL(2,R) is replaced by certain simple non-compact real Lie groups of higher rank. As for the usual Teichmuller space, these spaces consist entirely of discrete and faithful representations. Several cases have been identified over the years. First, the Hitchin components for split groups, then the maximal Toledo invariant components for Hermitian groups, and more recently certain components for SO(p,q). In this talk, I will describe a general construction of all possible higher Teichmuller spaces, and a parametrization of them using Higgs bundles given in joint work with Bradlow, Collier, Gothen and Oliveira.