Gordon Douglas Slade (born December 14, 1955, in

Toronto Toronto ( ; or ) is the capital city of the Canadian province of Ontario. With a recorded population of 2,794,356 in 2021, it is the most populous city in Canada and the fourth most populous city in North America. The city is the ancho ...

) is a Canadian mathematician, specializing in

probability theory Probability theory is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expressing it through a set o ...

Education

Slade received in 1977 his bachelor's degree from the

University of Toronto The University of Toronto (UToronto or U of T) is a public research university in Toronto, Ontario, Canada, located on the grounds that surround Queen's Park. It was founded by royal charter in 1827 as King's College, the first institution ...

and in 1984 his PhD for research supervised by Joel Feldman and Lon Rosen at the

University of British Columbia The University of British Columbia (UBC) is a public university, public research university with campuses near Vancouver and in Kelowna, British Columbia. Established in 1908, it is British Columbia's oldest university. The university ranks a ...

Career and Research

As a

postdoc A postdoctoral fellow, postdoctoral researcher, or simply postdoc, is a person professionally conducting research after the completion of their doctoral studies (typically a PhD). The ultimate goal of a postdoctoral research position is to p ...

he was a lecturer at the

University of Virginia The University of Virginia (UVA) is a Public university#United States, public research university in Charlottesville, Virginia. Founded in 1819 by Thomas Jefferson, the university is ranked among the top academic institutions in the United S ...

. From 1986 he was at

McMaster University McMaster University (McMaster or Mac) is a public research university in Hamilton, Ontario, Canada. The main McMaster campus is on of land near the residential neighbourhoods of Ainslie Wood and Westdale, adjacent to the Royal Botanical Ga ...

and since 1999 he is a professor at the University of British Columbia. He developed the technique of ''lace expansion'' (originally introduced by David Brydges and Thomas C. Spencer in 1985) with applications to probability theory and

statistical mechanics In physics, statistical mechanics is a mathematical framework that applies statistical methods and probability theory to large assemblies of microscopic entities. It does not assume or postulate any natural laws, but explains the macroscopic be ...

, such as self-avoiding random walks and their enumeration,

random graph In mathematics, random graph is the general term to refer to probability distributions over graphs. Random graphs may be described simply by a probability distribution, or by a random process which generates them. The theory of random graphs li ...

percolation theory In statistical physics and mathematics, percolation theory describes the behavior of a network when nodes or links are added. This is a geometric type of phase transition, since at a critical fraction of addition the network of small, disconnected ...

, and branched polymers. In 1989 Slade proved with Takashi Hara that the Aizenman– Newman triangle condition at critical percolation is valid in sufficiently high dimension. The Hara–Slade result has important consequences in

mean field theory In physics and probability theory, Mean-field theory (MFT) or Self-consistent field theory studies the behavior of high-dimensional random (stochastic) models by studying a simpler model that approximates the original by averaging over degrees of ...

. In 1991 Slade and Hara used the lace expansion to prove that the average distance covered in self-avoiding random walks in 5 or more dimension grows as the square root of the number of steps and that the scaling limit is

Brownian motion Brownian motion, or pedesis (from grc, πήδησις "leaping"), is the random motion of particles suspended in a medium (a liquid or a gas). This pattern of motion typically consists of random fluctuations in a particle's position insi ...

Honours and awards

Slade was an invited speaker in 1994 at the ICM in Zürich with lecture ''The critical behaviour of random systems''. Slade received in 1995 the

Coxeter–James Prize The Coxeter-James Prize is a mathematics award given by the Canadian Mathematical Society (CMS) to recognize outstanding contributions to mathematics by young mathematicians in Canada. First presented in 1978, the prize is named after two renown ...

and in the 2010 the

CRM-Fields-PIMS Prize The CRM-Fields-PIMS Prize is the premier Canadian research prize in the mathematical sciences. It is awarded in recognition of exceptional research achievement in the mathematical sciences and is given annually by three Canadian mathematics institu ...

. He was elected a

Fellow of the Royal Society of Canada Fellowship of the Royal Society of Canada (FRSC) is an award granted to individuals that the Royal Society of Canada judges to have "made remarkable contributions in the arts, the humanities and the sciences, as well as in Canadian public life ...

(FRSC) in 2000, in 2010 of the

Fields Institute The Fields Institute for Research in Mathematical Sciences, commonly known simply as the Fields Institute, is an international centre for scientific research in mathematical sciences. It is an independent non-profit with strong ties to 20 Ontari ...

, and in 2012 of the

American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...

and of the

Institute of Mathematical Statistics The Institute of Mathematical Statistics is an international professional and scholarly society devoted to the development, dissemination, and application of statistics and probability. The Institute currently has about 4,000 members in all parts o ...

. He was elected a

Fellow of the Royal Society Fellowship of the Royal Society (FRS, ForMemRS and HonFRS) is an award granted by the judges of the Royal Society of London to individuals who have made a "substantial contribution to the improvement of natural science, natural knowledge, incl ...

in 2017. In 2018 Slade was awarded the

Jeffery–Williams Prize The Jeffery–Williams Prize is a mathematics award presented annually by the Canadian Mathematical Society. The award is presented to individuals in recognition of outstanding contributions to mathematical research. The first award was presen ...

Selected publications

*with Neal Madras: ''Self-avoiding walk'', Birkhäuser 1993 *The lace expansion and its applications (École d’Eté de Probabilités de Saint-Flour XXXIV, 2004), Springer Verlag 2006http://www.math.ubc.ca/~slade/sf.pdf The lace expansion and its applications, pdf]

References

{{DEFAULTSORT:Slade, Gordon Douglas 1955 births Living people University of Toronto alumni University of British Columbia alumni Academic staff of the University of British Columbia Canadian mathematicians Fellows of the Royal Society of Canada Fellows of the American Mathematical Society Fellows of the Institute of Mathematical Statistics Probability theorists Canadian Fellows of the Royal Society