The Canadian Mathematical Society (CMS) has selected Martin Barlow as the recipient of the 2008 Jeffery-Williams Prize, Izabella Laba as the recipient of the 2008 Krieger-Nelson Prize, and Vinayak Vatsal as the winner of the 2007 Coxeter-James Prize.

The Jeffery-Williams Prize recognizes mathematicians who have made outstanding contributions to mathematical research.

Professor Martin Barlow is the leading international expert in the study of diffusions on fractals and other disordered media. He has made a number of profound contributions to a variety of fields including probabilistic methods in partial differential equations, stochastic differential equations, filtration enlargement, local times, measure-valued diffusions and mathematical finance.

In the 1980's he resolved a thirty year old problem with his derivation of necessary and sufficient conditions (the latter with John Hawkes) for the continuity of local time of a Lévy process. This was the resolution of a problem which had attracted the efforts of Hale Trotter, Ronald Getoor and Harry Kesten among others.

In the 1990's he carried out a detailed study of diffusions on a variety of fractal-like sets and derived precise upper and lower bounds on their heat kernels. This work laid the groundwork for a new area of study in probability which has attracted experts in Dirichlet forms, diffusions on manifolds and statistical mechanics. He currently is at the forefront of a program to study the transport properties of a broad class of graphs and manifolds. The original motivation for the study of diffusion on fractals came from the physics community who were interested in more general disordered random media but viewed typical fractals like the Sierpinski carpets and gaskets as good testing grounds for highly inhomogeneous media. Thanks in large part to the pioneering efforts of Martin Barlow the discipline has reached the point where the original objectives of the physicists are now within mathematical reach. Barlow remains at the leading edge of this research with his recent work giving sharp results for the behaviour of transition probabilities for random walks on super-critical percolation clusters.

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.

Past distinctions include the Rollo Davidson Prize from Cambridge University, the Junior Whitehead Prize from the London Mathematical Society and an invited lecture at the 1990 ICM in Kyoto. He has served the Canadian mathematical community on the Research Committee of the CMS and on the Editorial Board of the Canadian Journal Mathematics and the Canadian Mathematical Bulletin. He also has served on a number of international panels and editorial boards and recently finished a term as Editor-in-Chief of Electronic Communications in Probability. He is a Fellow of the Royal Society of Canada and in 2006 was elected Fellow of the Royal Society (London).

Dr. Barlow will present the 2008 Jeffery-Williams Prize Lecture at the CMS Summer Meeting in Montréal (June 2008).

The Krieger-Nelson Prize recognizes outstanding research by a female mathematician.

Izabella Laba has established a position as one of Canada's leading harmonic analysts. She has made major contributions to the Kakeya problem, and to the study of translational tilings and distance sets.

Although her current work is in harmonic analysis, Laba began her career working in on N-body scattering theory in mathematical physics. After obtaining her Ph.D. in 1994 at the University of Toronto with Michael Sigal she first attracted attention with her proof (with Christian Gérard) of asymptotic completeness for a large class of N-body systems in the presence of a magnetic field. This work became the subject of a monograph in the AMS mathematical surveys and monographs series.

During her time as Hedrick Assistant Professor at UCLA, Laba interests turned to harmonic analysis. A central problem in this field is the Kakeya conjecture concerning Besicovitch sets. A Besicovitch set is a subset of n-dimensional Euclidean space containing a line segment in every direction. The Kakeya conjecture states that such a set must have Minkowski and Hausdorff dimension n. This conjecture is linked to important open problems in harmonic analysis like the restriction conjecture and the Bochner-Riesz conjecture. To date, the best known lower bound on the dimension of a Besicovitch set in three dimensions is due to Katz, Laba and Tao.

After her time at University of California at Los Angeles (UCLA), Laba moved to Princeton and then in 2000 to the University of British Columbua where she was promoted to full Professor in 2005. Here she has continued her work in harmonic analysis, with important results in study of translational tilings and distance sets.

In addition to her research articles and the monograph mentioned above, Laba (with Carol Shubin) co-edited Thomas Wolff's "Lectures in Harmonic Analysis", which he had left uncompleted at the time of his death.

Laba's outstanding work has been recognized with a UBC Faculty of Science Achievement Award for Research in 2002 and the CMS Coxeter-James Prize in 2004.

Dr. Laba will present the 2008 Krieger-Nelson Prize Lecture at the CMS Summer Meeting in Montréal (June 2008).

The Coxeter-James Prize recognizes young mathematicians who have made outstanding contributions to mathematical research.

Dr. Vinayak Vatsal has made fundamental contributions to the Iwasawa Theory of elliptic curves, introducing profound techniques from ergodic theory into the subject and obtaining startling theorems on the non-vanishing of p-adic L-functions and mu-invariants that had previously been unobtainable by more orthodox analytic methods. His 2002 Inventiones paper on the uniform distribution of Heegner points led to the complete solution of a fundamental conjecture of Mazur concerning such L-functions (now the Vatsal-Cornut theorem). In the words of his referees, these results have "transformed our understanding of the ranks of elliptic curves in towers of number fields.

Dr. Vatsal received a Bachelor of Science degree in 1992 from Stanford University and a Ph.D. in 1997 from the Princeton University under the supervision of Professor Andrew Wiles. After a post-doctoral fellowship at the University of Toronto, he joined the University of British Columbia in 1999, where he is currently Associate Professor of Mathematics.

Dr. Vatsal was selected as a Sloan Fellow for 2002-2004, he received the 2004 André Aisenstadt Prize of the Centres de Recherches Mathématiques, the 2006 Ribenboim Prize of the Canadian Number Theory Association and was an invited speaker at the 2006 International Congress of Mathematicians in Madrid.

Dr. Vinayak Vatsal will present the 2007 Coxeter-James Prize Lecture at the CMS Winter Meeting hosted by the University of Western Ontario in December 2007.

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