- Groups acting on discrete structures such as trees and buildings, representations of such groups, linear groups over local fields;
- Automorphic forms;
- p-adic Hodge theory, p-adic modular forms;
- Cardinal functions and cardinal inequalities on topological spaces;
- Operator theory in Hilbert spaces;
- Coherent rings;
- The differentiability of convex functions with domains in locally convex spaces;
- Random walks on groups.
Harmonic analysis, functional analysis, analytic number theory, convex analysis and probability.
Dr D. I. Cartwright (D.Cartwright@maths.usyd.edu.au)