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UNIVERSITY OF REGINA Department of Mathematics & Statistics

Department of Mathematics & Statistics
Speaker: Michael Kozdron
Date: Friday, November 18, 2005
Time: 3:30 p.m.
Location: College West 307.18 (Math & Stats Lounge)
Title: An Introduction to the Schramm-Loewner Evolution
Abstract: The interplay between probability and complex analysis was really first exploited
by Paul L´evy in the 1950's who realized that two-dimensional Brownian motion was confor-
mally invariant. Since it had been proved earlier by Monroe Donsker that the scaling limit of
simple random walk is Brownian motion, we now had an example of a conformally invariant
scaling limit.
For the past several decades physicists and mathematicians have studied two-dimensional
discrete models with the hope of explaining some of the macroscopic properties of the asso-
ciated physical system. The Ising model of spin systems is such an example. One approach
to the analysis is to determine a scaling limit which is, hopefully, conformally invariant.
The so-called holy grail of this program is the self-avoiding walk, a model of polymer chains
introduced in the 1940's by the Nobel-prize winning physicist Paul Flory.
Recently, Oded Schramm combined an old equation of Charles Loewner's in complex analysis


Source: Argerami, Martin - Department of Mathematics and Statistics, University of Regina


Collections: Mathematics