Hitchin representations of Fuchsian groups

Abstract

We survey the theory of Hitchin representations of closed surface groups into $\mathsf{PSL}(d,\mathbb{R})$ with a focus on their dynamical and geometric properties. We then describe recent extensions of this work to study Hitchin representations of co-finite area Fuchsian groups. The motivation for this recent work is a conjecture about the geometry of the augmented Hitchin component.