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.

Intro
Positive tuples of flags
Cusped Hitchin representation
Very rough idea of proof
Bowen-Series coding: Example
Bowen-Series coding: General case General construction.
Bowen-Series coding: Technical issues
Bowen-Series coding: A fix
Nice countable Markov shifts
Quint's Iwasawa cocycle: General
Nice potentials: lengths
Nice potentials: entropy gap
Orbit counting theorem
Renewal theorem
Strategy: Partition into cylinders
Equidistribution/Motivation