An operator algebraic perspective on Teichmüller dynamics.

We aim to study Teichmuller dynamics in a noncommutative framework. In particular, we will look at Cuntz-Pimsner and groupoid C*-algebras that encode both the Teichmuller space and dynamics in a single algebraic structure. K-theoretic Invariants on these C*-algebras become invariants on the dynamical systems that can be reformulated in a dynamical context. The project seeks to exploit previous constructions in less complicated situations to drive our intuition. We believe a critical component may come from the work of Gadre et al, where they classified dynamics arising from a canonical cocycle that will provide a strongly continuous automorphism on the C*-algebras and could give rise to interesting KMS Equilibrium states and other invariants.