Hitchin representations of Fuchsian groups

Abstract

Dedicated to Dennis Sullivan on the occasion of his 80th birthday. Dennis was very kind to me when I was a feckless young mathematician and he continues to be an inspiration now that I am a feckless old mathematician.

Pressure metrics for cusped Hitchin components

“…We hope to eventually establish an analogue of Masur's result in the higher rank setting. (See [14] for a more detailed description of the conjectural geometric picture of the augmented Hitchin component. )…”