| 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).
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