Cusped Hitchin representations

Group Actions and Dynamics
Event time: 
Monday, February 22, 2021 - 4:00pm
Richard Canary
Speaker affiliation: 
University of Michican
Event description: 
We develop a theory of cusped Hitchin representations of
geometrically finite Fuchsian groups into SL(d,R). When d=3, cusped
Hitchin representations arise as holonomy maps of finite area real
projective surfaces. We develop general criteria for when one can obtain counting and equidistribution  results for potentials on countable Markov shifts. We show that these general criteria are satisfied by roof functions associated to linear functionals giving “length functions” for cusped  Hitchin representations. 
The long term goal of this project is to develop a metric theory of the
augmented Hitchin component which generalizes the fact that augmented
Teichmuller space is the metric completion of Teichmuller space with the
Weil-Petersson metric. (This is joint work with Tengren Zhang and Andy Zimmer,
and with Harry Bray, Nyima Kao and Giuseppe Martone).