PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

For more information about this meeting, contact Thomas Barthelme, Mari Royer, Anatole Katok, Federico Rodriguez Hertz, Dmitri Burago.

Title:Parametrizing Hitchin components
Seminar:Dynamical systems seminar
Speaker:Guillaume Dreyer, Notre-Dame University
Abstract:
Let S be a closed, connected, oriented surface of genus g>1. Hitchin components Hit_n(R) are components of the PSL_n(R)--character variety R_{PSL_n(R)}(S) that generalize Teichmuller components in the case where n=2. Over the recent years, groundbreaking work has revealed great geometric, dynamical and algebraic properties for the representations in Hit_n(R). In particular, these Hitchin representations turn out to share many features with the classic Fuchsian representations. In a joint work with Francis Bonahon, we construct a geometric, real analytic parametrization of Hitchin components Hit_n(R) The construction of this parametrization strongly relies on two independent approaches to studying Hitchin representations: the dynamical approach of Anosov representation, introduced by F. Labourie; and the algebraic-combinatorial approach of Positive representation, developed by V. Fock and A. Goncharov. In essence, our parametrization is an extension of Thurston's shear coordinates on the Teichmuller space, combined with Fock-Goncharov's coordinates on the moduli space of positive framed local systems of a punctured surface.

Room Reservation Information

Room Number:MB114
Date:04 / 14 / 2014
Time:03:35pm - 05:35pm