Research Interests: PDE analysis, in particular hyperbolic PDE. Classical general relativity.

I am interested in partial differential equations (PDE), with particular application to problems arising in general relativity. PDE are equations that describe how a certain quantity varies from place to place. For example, the wave equation describes how the pressure of the air in a room changes as a function of space and time as a sound wave passes through it. The study of such equations is central to many areas of modern mathematics and physics. The class of PDE that I mostly study arise from the study of general relativity. General relativity is Einstein's theory of the gravitational field in which it is postulated that space and time together form a dynamical geometry, which evolves in time according to a PDE whose character is similar to that of the wave equation. In particular, solutions exists describing propagating gravitational waves, a fact that was recently given spectacular experimental corroboration by the results of LIGO in September 2015.

I'm Professor of Mathematical Physics, with a joint appointment between the two departments of the Faculty of Mathematics: the Department for Pure Mathematics and Mathematical Statistics (DPMMS) and the Department of Applied Mathematics and Theoretical Physics (DAMTP).