I am a lecturer in the mathematics department and a member of the stochastic analysis research group.
I originally came to Swansea as an undergraduate and stayed to complete a Ph.D. in stochastic analysis under the supervision of Prof Aubrey Truman. After working in the insurance industry I returned to Swansea to take up my current post.
My research interests focus on probabilistic methods in mathematical physics particularly the relation between classical and quantum mechanics. Past topics include:
1. The semiclassical Coulomb/Kepler problem. This work began by considering the “atomic elliptic state”; a particular a stationary quantum state for the Coulomb problem which is concentrated on an ellipse. By considering the associated stochastic mechanics we have been able to provide a derivation of classical Keplerian motion in the semiclassical limit. This has lead to several papers investigating various aspects of semiclassical Coulomb problems.
2. Semiclassical asymptotics for heat and Burgers equations. This work has its origin in the Hamilton-Jacobi theory developed by A. Truman and D. Elworthy to investigate the semiclassical limit of heat and Schrodinger equations using classical mechanics. These ideas have been developed to include stochastic heat and Burgers equations and I initially worked on the analysis of the behaviour of singularities in the solution for the stochastic Burgers equation. More recently we have worked on extending these results to heat and Burgers equations including vector potentials.
Current research interests cover the above areas but also include stochastic analysis and graded algebras (joint with E. Beggs) and phase space path integrals (joint with A. Truman).
I am also involved in range of teaching and have taught courses including classical mechanics, Hamiltonian and Lagrangian mechanics, electro-magnetics, differential equations and mathematical modelling. I regularly supervise M.Sc. projects on mathematical finance.