# The 2010 CRM-Fields-PIMS Prize is awarded to Gordon Slade

The Directors of the three Institutes, CRM, Fields and PIMS, are pleased to announce that Gordon Slade from the University of British Columbia is the recipient of the 2010 CRM-Fields-PIMS Prize.

The award recognises his outstanding work in rigorous statistical mechanics and probability. He is renowned for developing a technique known as the lace expansion into a systematic calculus which he has applied to diverse and famous problems including self-avoiding walk, percolation, branched polymers, random graphs, and numerical techniques for the exact enumeration of self-avoiding walks.

In 1992 Hara and Slade proved that in five or more dimensions the end-to-end distanceof self-avoiding walk grows according to the same √n law exhibited by simple random walk and that the scaling limit of self-avoiding walk is Brownian motion.

In 1989 Hara and Slade proved that the Aizenman-Newman triangle condition holds for critical percolation in high dimensions. The triangle condition implies a large collection of properties for the critical cluster that are collectively summarised by the term “mean field theory”. Since this initial impetus a quite complete understanding of critical percolation clusters in high dimensions has grown out of work with his co-authors Derbez, Hara, van der Hofstad and den Hollander. In particular, the scaling limit of oriented percolation is super-Brownian motion and the existence and the properties of the incipient infinité percolation cluster have been established in certain cases. By related methods, Slade and his co-authors have established a very complete description of the critical window for the Hamming cube with randomly deleted edges.

These results address the most difficult problems in central areas of probability andstatistical physics. These are questions motivated by physical problems which are easy to state and notoriously difficult to solve. The use of the lace expansion to establish mean field behaviour for self-avoiding walk and critical percolation above the critical dimension is one of the major developments in probability in the last 15 years.

Gordon Slade received his undergraduate degree from the University of Toronto in 1977 and completed his Doctoral degree with Lon Rosen and Joel Feldman at the University of British Columbia in 1984. He was Lecturer at the University of Virginia from 1985 to 1986. In 1986 he joined the faculty of McMaster University and since 1999 he has been Professor of Mathematics at the University of British Columbia.

Gordon Slade has been a leader in Canadian Mathematics, having been an organiser of the (98-99) thematic year in probability and its applications at the Fields Institute, co-organiser of the recent CRM-PIMS Programme Challenges and Perspectives in Probability (08-09). He has served on scientific panels of the Fields and Pacific Institutes and is currently a member of the Editorial Board of the Canadian Journal of Mathematics. His stature as one of the world’s leading probabilists and mathematical physicists was underlined by his 1994 invitation to the International Congress of Mathematics and his 2004 invitation to lecture at the prestigious St. Flour Summer School.