Noncommutative analysis is an area of mathematics in which we seek to model and understand complex systems using algebras of operators on Hilbert space. Operator algebras originated in the study of quantum theory, and their structure incorporates facets of many areas of mathematics including algebra, measure theory, topology, differential geometry and others. Ever since they first appeared, operator algebras have proven to be a potent mathematical tool in applications both within and outside mathematics. In the Centre for Noncommutative Analysis we are particularly interested in the structure of C*-algebras and their uses in representation theory and invariants for topological dynamical systems, as well as their applications in geometry and in mathematical physics.
Research focus
- Constructive Kasparov product and its applications in geometry and dynamics
- Curvature for operator algebras and quantum systems
- Applications of index theory to geometry and physics
- Topological aspects of higher rank graphs and their C*-algegbras
- KMS states on classes of C*-algberas
- C*-algebras associated to graphs of groups
- Groupoid C*-algebras
Members
- Associate Professor David Pask (Director)
- Professor Alan Carey
- Associate Professor Adam Rennie
- Dr Adam Sierakowski
- Prof. Aidan Sims
- Dr Ben Whale
Associate members
- Dr Nathan Brownlowe (University of Sydney)
- Professor Alex Kumjian (University of Nevada, Reno)
- Professor Jacqui Ramagge (University of Sydney)