Picture of a simulated branching Brownian motion.
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detailed picture and description.
My general research interests lie in probability theory. I have a broad interest throughout this field, including
modeling and applications of stochastic processes, although my research has
tended to concentrated on the theoretical side. I also enjoy membership of Bath's
Centre of Mathematical Biology where interesting probabilistic models of
biological processes often come to light.
My main focus is on branching
diffusions - which can roughly be thought of as models for populations of
'animals' which breed, die and move around in space. This work often involves the inter-play of probability with
mathematical analysis through links with non-linear partial differential
equations. For example, one aim has been to prove results about travelling-wave
solutions of reaction-diffusion equations via probabilistic methods by studying
corresponding branching diffusion models. Related models have been applied to diverse problems from
chemical and physical reactions, population genetics and geology.
Some key words of interest are: