UBC mathematician Martin Barlow--the leading international expert in diffusion on fractals--has been awarded the 2009 CRM-Fields-PIMS Prize. The award, presented by the Centre de recherches mathematiques, the Fields Institute and the Pacific Institute for the Mathematical Sciences, is worth $10,000 and intended to be the premier mathematics prize in Canada.
Barlow is a leading figure in probability and the foremost international expert in diffusion on fractals and other disordered media. His work has been important in such diverse fields as partial differential equations, including major progress on the De Giorgi conjecture, stochastic differential equations, the mathematical finance of electricity pricing, filtration enlargement and branching measure diffusions.
Barlow's work in the 1980's helped solve a 30-year-old problem in probability theory which had attracted the efforts of mathematical luminaries such as Hale Trotter, Ronald Getoor and Harry Kersten. That work paved the way for the study of the connection between local times and Gaussian processes.
In the 1990's his detailed study of diffusions on a variety of fractals and fractal-like sets opened a new area of study in probability, making him the leading international expert in the area. Barlow remains at the leading edge of the field.
Among other honours, Barlow has received the Jeffery-Williams Prize of the Canadian Mathematical Society, the Rollo Davidson Prize from Cambridge University, and the Junior Whitehead Prize from the London Mathematical Society.