I am a retired member of staff in the School of Mathematics.
My main research is in the areas of Dynamical Systems, particularly the application of complex methods to exponential asymptotics arising in the study of codimension-two bifurcations and renormalisation, and Stochastic Analysis, particularly questions of existence, uniqueness and approximation of solutions of Stochastic Differential Equations.
I also have some interest in applications of analysis to PDE, complexity of matrix multiplication and applications of mathematics to biology, particularly protein folding.
Uniqueness of solutions of stochastic differential equations, IMRN 2007 No. 24, Art. ID rnm124. pdf
Differential equations driven by rough paths: an approach via discrete approximation, AMRX 2007 No. 2, Art. ID abm009. pdf
(with A. J. Stothers) Improved bound for complexity of matrix multiplication, Proc. Roy. Soc. Ednburgh Sect. A 143 (2013), 351-369. pdf
KMT theory applied to approximations of SDE, in Stochastic Analysis and Applications, Springer 2014 (Proceedings of conference in Oxford in September 2013, in honour of Terry Lyons' 60th birthday). pdf
Pathwise approximation of stochastic differential equations using coupling (updated 28/5/2015). pdf
Polynomial perturbations of normal distributions (updated 25/9/2017). pdf