# Geometry and Topology Seminar

Friday, October 4, 2019
3:00pm to 5:00pm
Linde Hall 187
Harmonic maps for Hitchin representations
Qiongling Li, Chern Institute of Mathematics, Nankai University,

Hitchin representations are an important class of representations of fundamental groups of closed hyperbolic surfaces into PSL(n,R), at the heart of higher Teichmüller theory. Given such a representation j, there is a unique j-equivariant harmonic map from the universal cover of the hyperbolic surface to the symmetric space of PSL(n,R). We show that its energy density is at least 1 and that rigidity holds. In particular, we show that given a Hitchin representation, every equivariant minimal immersion from the hyperbolic plane into the symmetric space of PSL(n,R) is distance-increasing. Moreover, equality holds at one point if and only if it holds everywhere and the given Hitchin representation j is an n-Fuchsian representation.