Geometry Seminar

Date: March 8, 2019

Time: 4:00PM - 5:00PM

Location: BLOC 628

Speaker: Giuseppe Martone, University of Michigan

Title: Hitchin representations and positive configurations of apartments

Abstract: Hitchin singled out a preferred component in the character variety of representations from the fundamental group of a surface to PSL(d,R). When d=2, this Hitchin component coincides with the Teichmuller space consisting of all hyperbolic metrics on the surface. Later Labourie showed that Hitchin representations share many important differential geometric and dynamical properties. Parreau extended previous work of Thurston and Morgan-Shalen to a compactification of the Hitchin component whose boundary points are described by actions of the fundamental group of the surface on a building. In this talk, we offer a new point of view for the Parreau compactification, which is based on certain positivity properties discovered by Fock and Goncharov. Specifically, we use the Fock-Goncharov construction to describe the intersection patterns of apartments in invariant subsets of the building that arises in the boundary of the Hitchin component.