Originally from Aberystwyth, I completed my BSc in Pure Mathematics at Swansea University, followed by an MRes in Stochastic Processes at the same department. During my MRes I worked with Dr Kristian Evans on pseudo-differential operators on the torus that extend to generators of Feller processes. After that, I completed an MSc at Warwick (MASDOC) taking modules from Analysis, Probability, Statistics and Numerical Analysis. For my MSc project I looked at a class of Markov processes on bounded domains generated by certain pseudodifferential operators.
I am currently in my second PhD year under the supervision of Professor Vassili Kolokoltsov and Dr Larbi Alili, investigating generators of Feller processes on bounded domains. More specifically, I am looking at processes that live in a bounded domain, whose generator can be thought of as a generalization of certain fractional derivatives (Caputo and Riemann-Liouville derivatives). Using this probabilistic view point, one can look at certain equations involving these (generalised) fractional operators and thus obtain a probabilistic interpretation of the solution to such equations. I am also interesting in estimates for Green's functions of certain time-fractional evolution equations. These papers will be on arXiv soon.
My mathematical interests lie mainly in Probability and Analysis.
I am currently the chairman of the MASDOC student staff liason committee (SSLC). I am also a PhD representative on the Welfare and Communications Committe (WCC) in the Statistics department.