This project is in pure mathematics, specifically relating to functional analysis and operator algebras, and will explore how to use operator algebras to extract new invariants of dynamical systems: features of the systems which distinguish one from another. Specifically, we will combine groupoid theory and C*-correspondence theory to associate highly tractable new operator algebras to dynamical systems, and then investigate how index theory, duality theory and ideas from noncommutative geometry can be used to extract powerful new dynamical invariants. The project will develop new relationships between groupoid and Cuntz-Pimsner constructions, and investigate dynamics which encode novel examples of operator-algebraic Poincare duality.

This project is in pure mathematics, specifically relating to functional analysis and operator algebras, and will explore how to use operator algebras to extract new invariants of dynamical systems: features of the systems which distinguish one from another. Specifically, we will combine groupoid theory and C*-correspondence theory to associate highly tractable new operator algebras to dynamical systems, and then investigate how index theory, duality theory and ideas from noncommutative geometry can be used to extract powerful new dynamical invariants. The project will develop new relationships between groupoid and Cuntz-Pimsner constructions, and investigate dynamics which encode novel examples of operator-algebraic Poincare duality.