Teichmüller theory is a fascinating interplay between complex geometry and topology: Teichmüller space is both a space of complex structures on a surface $S$ and a connected component $\chi(\mathsf{PSL}(2,\mathbb R))$ of representations of $\pi_1(S)$ in $\mathsf{PSL}(2,\mathbb R)$. For a general (simple real split) group $\mathsf{G}$, a similar connected component $\chi(\mathsf G)$, called the {\em Hitchin component} and its Thurstonian dynamical geometry has attracted a lot of attention recently. Yet, the complex interpretation of the Hitchin component is largely unknown (although conjectured). In this talk, I will explain the complex interpretation of Hitchin components for rank 2 groups as a space of pairs $(J,q)$ where $J$ is a complex structure on $S$ and $q$ a holomorphic differential of an order depending on the group $\mathsf G$. I will use and explain Hitchin--Corlette major results on non abelian Hodge theory.
Donnerstag, den 15. Mai 2014 um 09.15 Uhr Uhr, in INF 288, HS 3 Donnerstag, den 15. Mai 2014 at 09.15 Uhr, in INF 288, HS 3
Der Vortrag folgt der Einladung von The lecture takes place at invitation by Prof. Dr. Anna Wienhard