I give tutorials and lectures in most areas of pure mathematics: analysis (the rigorous study of general properties of limits and functions, including differentiation and integration), algebra, topology, set theory and logic. When I was an undergraduate, my regular tutorial partner was Andrew Wiles (yes, the one who proved Fermat's Last Theorem), so I know how it feels to be paired with someone cleverer than oneself!
In order to be different from Andrew Wiles, as an undergraduate I looked for optional courses away from number theory, and I picked a course in functional analysis almost at random and I happened to enjoy it. Consequently, I have been working in (functional) analysis ever since I started as a research student. Nowadays my research is in operator theory methods for (partial) differential equations, especially the types of equations involving time and space variables which are typical of models arising in mathematical physics, engineering and biology.
Specialist interests have included semigroups and algebras of linear operators on infinite-dimensional spaces (Banach spaces, Hilbert spaces), long-time asymptotic behaviour, and functional calculus of unbounded operators.