I will be starting a Fellowship at Christ Church from the beginning of Michaelmas Term 2010 with responsibility for some of the core undergraduate teaching in pure mathematics. Currently, I am an EPSRC-funded postdoc working in the stochastic analysis group at the Mathematical Institute and a member of the Oxford-Man Institute of Quantitative Finance. Before coming to Oxford I read mathematics as an undergraduate at St. John's College, Cambridge where I subsequently studied Part III of the mathematical tripos before completing my Ph.D. at the Department of Pure Mathematics and Mathematical Statistics.
My interests span a range of mathematical areas arising in the study of probability and stochastic (random) processes and especially in the theory of stochastic differential equations. Typically, the equations one is interested in describe the behaviour of some output process under the control of a randomly evolving input signal; such models are ubiquitous across applied mathematics from theoretical physics to mathematical finance. However, their properties as purely mathematical objects are also fascinating and a rich and satisfying theory has been developed over the past fifty years. Much of my work exploits ideas in the recently developed theory of rough paths, which has provided new ways to think about random processes and has extended the frontiers of the subject dramatically. The techniques of this theory have yielded fresh insights into a range of applications including a description of turbulent fluids and the efficient simulation of option price sensitivities.
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