I research into differential equations, mostly PDEs, and their applications. Much of my work concerns diffusion-type equations and I am particularly interested in blow-up, as can model explosions or ignition, free-boundary problems, such as phase-change models, and models with non-local terms I am also interested in mathematical modelling of industrial, societal, and other problems, from bread baking and welding to homelessness and housing allocation. Many of these research areas originate through interaction with the Industrial Mathematics KTN and particularly the Study Groups with Industry.

I received my D.Phil. in mathematics at Oxford in 1979, then held post-doctoral fellowships, in both Oxford and Wellington. My work in this period concerned: Free-boundary problems, including both freezing/melting and the famous Hele-Shaw problem. Ignition, using both ODE and parabolic-equation models. A high-order parabolic model for thin-film flow. I was appointed lecturer at Heriot-Watt in 1982, reader in 1987, professor in 1996, and elected fellow of the Royal Society of Edinburgh in 1990. Here I have continued my earlier research, proving key results on blow-up for parabolic equations, and on free-boundary motion. Largely through participation in Study Groups with Industry, I have also studied diverse practical problems: Industrial, including calorimetry, bread crusts and green roofs (collaborating companies have been small, SMEs, and large, such as RHM). Scientific, such as fire spread. Social, such as homelessness levels.