Uniformization for Hitchin representations

Abstract: After recalling the definition of Hitchin representations, and why the space of Hitchin representations carries many similarities with Teichmüller space, I will explain briefly Hitchin parametrisations and how minimal surfaces enterthe picture naturally, as well as some properties of the natural map from thespace of equivariant minimal surfaces into the Hitchin component.

I will then explain the main itching question that the conjecture was supposed to solve: find a complex interpretation, invariant under the mapping class group,of the Hitchin component, as well as describing the topology of the Hitchin moduli space.If time permits, I will explain a construction by Sambarino and myself, of a mapping classgroup invariant map from Hitchin component to Teichmüller space and how thisrelates to holomorphic differentials.

differential geometrydynamical systemsgeometric topology

Audience: researchers in the topic

Comments: Go to gear.math.illinois.edu/GEARtownEvents.html for more information

---

GEARtown Events: The Labourie Conjecture

Series comments: Go here for more information: gear.math.illinois.edu/GEARtownEvents.html

---