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.
Titles of talks given
- 'Fractional evoloution equations' - Speed talk at British Mathematical Colloquium, University of St Andrews, 11-14 June 2018.
- 'Fractional evolution equations and related two-sided estimates' - Postgraduate seminar, University of Warwick, 6 June 2018.
- 'Probabilistic methods in fractional calculus' - MASDOC Retreat, Peak District, 29 April - 2 May 2018.
- 'Two-sided estimates for the Greens function of fractional evolution equations' - Inequalities in PDEs/SPDEs, Bedlewo, Poland, 22-28 April 2018.
- 'Multidimensional fractional derivatives as generators of Feller processes on bounded domains', Bielefeld-Edinburgh-Swansea Stochastics Workshop, Bielefed, 26-28 March 2018
- 'Heat kernel estimates for fractional evolution equations' - International Conference on Stochastic Analysis and Applications, Bielefeld, 3-7 September 2018
- 'Heat kernel estimates for fractional evolution equations' - Probability and NonLocal PDE's, Swansea, 17-19 September 2018
- 'Fractional evolution equations and related estimates' - FCPNLO, Bilbao, September 26-28 2018