University of Surrey, PhD, Mathematics and Statistics

Research topics include: probabilistic properties of deterministic systems, including statistical limit laws; estimates for rates of decay of correlations; development of new methods for finding continuous and discrete symmetries of both differential and difference equations; effects of symmetries on stability, bifurcations and dynamics: for example, symmetry breaking, symmetric chaos, robust heteroclinic cycles, Hamiltonian and multi-symplectic systems, non-compact symmetry groups; development of numerical methods adapted to integrating symmetric systems and computing their bifurcation diagrams; turbulent behaviour in fluids, including a new approach to estimating the smallest length scales in the flows; the analysis of PDEs arising in population dynamics, for example, the positivity of solutions of high-order diffusion models; dynamical systems methods applied to coherent structures representing interfaces between stable, spatially periodic structures with possibly different spatial wave numbers; rigorous instability results for periodic waves and multi-periodic patterns;quasi-periodic patterns on the ocean surface, atmospheric flows;age-structured models with spatial effects including advection and diffusion, resulting in partial differential equations with delays;disease modelling and other aspects of mathematical medicine include studies of the spatial spread of tuberculosis and SARS;The mechanics of myosin V, a molecular motor involved in intra-cell cargo transport; development of pilot procedures for use at the planning stage to assess the vulnerability of a design to become disconnected; investigations of graphical approaches for verifying disconnectivity of single or multi-treatment row column designs; development of computational algorithms for the identification and specification of rank reducing observation sets in various types of experimental design.