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Geometric Analysis Seminar

Higgs bundles and higher Teichmüller spaces

Oscar Garcia-Prada - Institute of Mathematical Sciences

Location:  zoom
Date & time: Tuesday, 23 February 2021 at 2:50PM - 3:50PM

Abstract: It is well-known that the Teichmüller 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 Teichmüller 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 Teichmüller 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 Teichmüller spaces, and a parametrization of them using Higgs bundles given in joint work with Bradlow, Collier, Gothen and Oliveira.