PhD in Pure Mathematics

Operator algebras is an active area of research with deep connections to other areas of mathematics such as topology, representation theory, and topological dynamics. One of the most important classes of operator algebras are C*-algebras, which are operator-norm closed subalgebras of the bounded linear operators on a complex Hilbert space that are closed under taking adjoints. This project will focus on C*-algebras arising from considerations in topological dynamics, algebra, or group theory. The research problem will be co-created with the student to align with their background and interests. Example topics include: Groupoid models for C*-algebras; Cartan subalgebras of C*-algebras; Semigroup C*-algebras; Ring C*-algebras; C*-algebras from algebraic actions.