Dynamics of cusped Hitchin representations

Geometric Group Theory Seminar
December 7, 2023
1:50PM - 2:50PM
MW 152

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Add to Calendar 2023-12-07 13:50:00 2023-12-07 14:50:00 Dynamics of cusped Hitchin representations Title:  Dynamics of cusped Hitchin representations Speaker:  Giuseppe Martone (Sam Houston State University) Abstract:  Cusped Hitchin representations are generalizations of finite-area hyperbolic structures on a surface with cusps. They arise naturally in the context of higher rank Teichmüller theory, and, in this talk, we will focus on their dynamical properties. Specifically, in joint work with Bray, Canary, and Kao, we connect these surface group representations to the dynamics of countable Markov shifts and potentials with desirable (thermo)dynamical properties. Using these tools, we obtain orbit counting results for cusped Hitchin representations. MW 152 Department of Mathematics math@osu.edu America/New_York public

Title:  Dynamics of cusped Hitchin representations

Speaker:  Giuseppe Martone (Sam Houston State University)

Abstract:  Cusped Hitchin representations are generalizations of finite-area hyperbolic structures on a surface with cusps. They arise naturally in the context of higher rank Teichmüller theory, and, in this talk, we will focus on their dynamical properties. Specifically, in joint work with Bray, Canary, and Kao, we connect these surface group representations to the dynamics of countable Markov shifts and potentials with desirable (thermo)dynamical properties. Using these tools, we obtain orbit counting results for cusped Hitchin representations.

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