 
Summary: UNIVERSITY OF REGINA
Department of Mathematics & Statistics
Colloquium
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 SchrammLoewner Evolution
Abstract: The interplay between probability and complex analysis was really first exploited
by Paul L´evy in the 1950's who realized that twodimensional 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 twodimensional
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 socalled holy grail of this program is the selfavoiding walk, a model of polymer chains
introduced in the 1940's by the Nobelprize winning physicist Paul Flory.
Recently, Oded Schramm combined an old equation of Charles Loewner's in complex analysis
