Orbit Counting Theorem for Cusped Hitchin Representations
Explore the dynamics of cusped Hitchin representations in this advanced mathematics lecture. Delve into the encoding of these representations using locally Holder continuous, eventually positive, non-arithmetic potentials with entropy gaps at infinity on topologically mixing countable Markov shifts. Learn about the orbit counting theorem for this class of shifts and potentials, and its application to cusped Hitchin representations. Follow the presentation as it covers topics such as positive tuples of flags, Bowen-Series coding, nice countable Markov shifts, Quint's Iwasawa cocycle, nice potentials, and the renewal theorem. Gain insights into the technical aspects of the proof, including the strategy of partitioning into cylinders and equidistribution. This joint work by Giuseppe Martone, Harry Bray, Dick Canary, and Nyima Kao offers a deep dive into advanced mathematical concepts at the intersection of geometry, dynamics, and representation theory.