I am happy to supervise students at any level, on topics related to current aspects of my research program. The specific project is decided through a discussion with the student, based on background, interests, and opportunities (e.g. availability of a new result, current research activity arising from conferences or visitors). For Honours/Master level projects, I expect knowledge of functional and/or stochastic analysis (as taught at ANU through "Functional Analysis and Spectral Theory" and "Stochastic Analysis with Financial Applications"). For PhD students, I look for an outstanding background in harmonic, functional, and/or stochastic analysis, an interest in PDE, and a theory building mentality.
For a list of my previous students (Honours level and above) and postdoctoral collaborators, including links to theses/web pages, see my supervision page.
My teaching activities (especially special topics courses and undergraduate PhB supervision) can also give you a good idea of what projects with me are about; see my teaching page.