An operator algebraic perspective on Teichmüller dynamics.
Lead Research Organisation:
University of Glasgow
Department Name: School of Mathematics & Statistics
Abstract
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.
Organisations
People |
ORCID iD |
Michael Whittaker (Primary Supervisor) | |
David Watt (Student) |
Studentship Projects
Project Reference | Relationship | Related To | Start | End | Student Name |
---|---|---|---|---|---|
EP/W523823/1 | 01/10/2021 | 30/09/2025 | |||
2608549 | Studentship | EP/W523823/1 | 01/10/2021 | 30/09/2025 | David Watt |