An operator algebraic perspective on Teichmüller dynamics.

我们的目标是在非对易框架下研究Teichmuller动力学。特别是，我们将研究Cuntz-Pimsner和广群C*-代数，它们将Teichmuller空间和动力学编码在一个单一的代数结构中。这些C*-代数上的K-理论不变量成为动力系统上的不变量，可以在动力学上下文中重新表达。该项目试图在不太复杂的情况下利用以前的结构来驱动我们的直觉。我们相信一个关键的组成部分可能来自Gadre等人的工作，他们将动力学分类为典型的上循环，这将在C*-代数上提供一个强连续的自同构，并可能产生有趣的KMS平衡态和其他不变量。

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.