Higher Complex Structures and Hitchin Components

Geometry Topology Seminar
Monday, January 30, 2023 - 2:00pm for 1 hour (actually 50 minutes)
Skiles 006
Alex Nolte – Rice/Georgia Tech
John Etnyre

A source of richness in Teichmüller theory is that Teichmüller spaces have descriptions both in terms of group representations and in terms of hyperbolic structures and complex structures. A program in higher-rank Teichmüller theory is to understand to what extent there are analogous geometric interpretations of Hitchin components. In this talk, we will give a natural description of the SL(3,R) Hitchin component in terms of higher complex structures as first described by Fock and Thomas. Along the way, we will describe higher complex structures in terms of jets and discuss intrinsic structural features of Fock-Thomas spaces.