Geometry MMA Seminar: Countable Markov shifts for cusped Hitchin representations

Speaker: Harry Bray, George Mason University

Title:   Countable Markov shifts for cusped Hitchin representations

Abstract:  I will discuss how a hyperbolic metric on a closed (finite area) surface can be determined by a suspension flow over a (countable) Markov shift via the geodesic flow. This construction generalizes to other geometries such as cusped Hitchin representations, and applications include counting results and equidistribution of closed curves. Along the way I intend to explain what all these objects are and provide illuminating examples. Fair warning: audience members will benefit from some familiarity with hyperbolic geometry. This is based on joint work with Canary, Kao, and Martone.

Time: Monday, September 19, 2022 – 1:30pm-2:30pm

Place: Exploratory Hall, Room 4208