# Martin Barlow is the 2009 CRM-Fields-PIMS Prize Recipient

The Directors of the three Institutes, CRM, Fields and PIMS are pleased to announce that Martin Barlow from UBC is the recipient of the 2009 CRM-Fields-PIMS Prize. Martin Barlow is a leading figure in probability and the leading international expert in diffusion on fractals and other disordered media. In addition, the impact of 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.

Already in the 1980’s, Martin Barlow settled a long open problem of probability theory, by providing necessary and sufficient conditions (the latter with J. Hawkes) for the continuity of local times of Lévy processes. This was the resolution of a thirty-year old problem which had attracted the efforts of Hale Trotter, Ronald Getoor and Harry Kersten among others. His conditions have 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 behaviour of diffusions on fractals and other disordered media. The study of the diffusion on the Sierpinski carpet, started with Ed Perkins and then Richard Bass in 1986, served as a testing ground for diffusion in highly inhomogeneous media, a domain of interest for the physics community which is now within mathematical reach. Barlow remains at the leading edge of this research with his recent work giving best possible results for the behaviour of transition probabilities for random walks on super-critical percolation clusters. The pioneering papers on the diffusion on the Sierpinski carpet attracted to the domain experts in Dirichlet forms, diffusions on manifolds and statistical mechanics. Martin Barlow currently is at the forefront of a program to study the transport properties of a broad class of graphs and manifolds.

Martin Barlow received his undergraduate degree from Cambridge University in 1975 and completed his Doctoral degree with David Williams at the University College of Swansea in Wales in 1978. He held Royal Society University Research Fellowship at Cambridge University from 1985 to 1992, when he joined the Mathematics Department at University of British Columbia. He currently is Professor of Mathematics at UBC. He has held a number of visiting professorships at leading universities including University of Tokyo, Cornell University, Imperial College, London, and Université de Paris.

Martin Barlow gave an invited lecture at the 1990 ICM in Kyoto and was an invited lecturer at the prestigious St. Flour Summer School in 1995. In 2008 he received the Jeffery-Williams Prize of the Canadian Mathematical Society. Other past distinctions include the Rollo Davidson Prize from Cambridge University, the Junior Whitehead Prize from the London Mathematical Society. He has been a leader of the international probability community, as a lead organizer of numerous conferences, Associate Editor of all the top probability journals and Editor-in-Chief of the Electronic Communications in probability. He is a Fellow of the Institute of Mathematical Statistics since 1995, of the Royal Society of Canada since 1998 and in 2006 was elected Fellow of the Royal Society (London).