Colloquium-Hitchin representations of Fuchsian groups

Speaker: Prof. Dick Canary (University of Michigan)

Time: Friday Nov/18, 2 pm — 3 pm 

Location: Phillips Hall B152

Title: Hitchin representations of Fuchsian groups

Abstract: The Hitchin component of representations of a closed surface group into SL(d,R) is one of the primary  examples of a Higher Teichmuller space (a component of the space of representations of a surface group into a Lie group which consists entirely of discrete, faithful representations). We will survey this theory and then  discuss a theory  of cusped Hitchin representations of geometrically finite Fuchsian groups into SL(d,R). These cusped Hitchin representations arise naturally by ``pinching''  classical Hitchin representations. We show that cusped Hitchin representations are cusped Borel Anosov and establish counting and equidistribution results.

The long term goal of this project is to develop a metric theory of the augmented Hitchin component which generalizes the fact that augmented Teichmuller space is the metric completion of Teichmuller space with the Weil-Petersson metric. (This is joint work with Harry Bray, Nyima Kao and Giuseppe Martone and with Tengren Zhang and Andy Zimmer).