Cusped Hitchin representations

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).