Colloquium and PIMS Distinguished Chair Lecture
3:30 p.m., Friday
Math 100
David Brydges
Pacific Institute for the Mathematical Sciences, UBC
and
University of Virginia
Self Avoiding Walk and Differential Forms
The continuous time simple random walk on a finite lattice will be
reviewed. Any such walk defines a collection of local times
\tau_{x}  the times spent at lattice sites x. There is an
isomorphism relating these local times to finite dimensional integrals
involving differential forms \phi \bar{\phi} + d\phi d\bar{\phi}.
This is called the ``supersymmetric representation'' in physics. In
principle the selfavoiding walk problem can be solved by approximately
evaluating such integrals, provided the approximation is uniform in
the dimension of the integral. The physicists have developed a far
reaching extension of "Laplaces's method" which appears to be uniform
in dimension. Formulas for coefficients in this approximation lead to
the famous Feynman graphs.
Refreshments will be served in Math Annex Room 1115, 3:15 p.m.
