David Brydges | PIMS - Pacific Institute for the Mathematical Sciences

Professor of Mathematics (retired), University of British Columbia

David Brydges received the PhD in 1976 at the University of Michigan under the direction of Paul Federbush. He held a postdoctoral position at Rockefeller University working for James Glimm. In 1978 he became Assistant Professor at the University of Virginia. He was promoted to Full Professor of Mathematics and Physics in 1981 and became Commonwealth Chair in 1996. He was recently appointed as a Canada Research Chair at the University of British Columbia.

Brydges received the Alfred P. Sloan Research fellowship in 1982. He has given lectures throughout the world including courses in the Troisiéme Cycle at Lausanne in 1992, Centre Emile Borel in 1998 and the Nach Diplom program at ETH, Switzerland. He is the President of the International Association of Mathematical Physics.

His interests are centered on the renormalization group with applications to quantum field theory, statistical mechanics and probability.

He was a member of the PIMS SRP from 2002-2007.

I will describe recent results on a connection between the so-called reconstruction problem on Markov random fields on trees and two important problems in computational evolutionary biology: the inference of ancestral states and the estimation of...

Abstract The Mayer expansion is a power series expansion that has a central place in statistical mechanics. It is also full of combinatorial miracles that relate it to graphs, forests and branched polymers. I will discuss the background, the results...

I will review connections, including the Dynkin isomorphism, between the Gaussian free field on a lattice and local time of random walk. These connections give useful representations for walks with self-interactions.

In the first lecture of this series the square of a Gaussian field was related to the local time of random walk and a Poisson process of random loops. In this lecture I will show how to "get rid" of the loops and end up with a representation for self...

In the second lecture I reviewed differential forms and then related the square of a differential form to the local time of random walk. In this lecture I will prove this result in more detail and illustrate the idea by explaining why certain...