From: Kelli McGee \(Kelly Services Inc\) (a-kellim@microsoft.com)
Date: Fri Feb 27 2004 - 14:03:52 PST
You are invited to attend...
************************************************************************
*****************************
WHO: Wendelin Werner
AFFILIATION: University of Paris-Sud in Orsay
TITLE: Brownian loop-soup, SLE and conformal field theory
II.
WHEN: Thu 3/11/2004
WHERE: 113/1021 Research Lecture Room, Microsoft Research
TIME: 3:30PM - 5:30PM
HOST: Oded Schramm and Scott Sheffield
************************************************************************
******************************
ABSTRACT:
Critical two-dimensional systems from statistical physics are believed
to behave in a conformal invariant way in their scaling limit.
Theoretical physicists in the late 70's and 80's have proposed to use
conformal field theory to study these scaling limits. In particular, the
set of critical exponents (and some correlation functions) are
classified according to the central charge of the model, that can they
view as the central charge of corresponding representations of an
infinite-dimensional Lie algebra, the Virasoro Algebra. The mathematical
understanding of these critical systems was limited until Oded Schramm
proposed to construct the scaling limit of interfaces in these systems
via interations of random conformal maps, that define the SLE curves and
led to various developments.
The goal of these two lectures is to explain a way to make sense of
conformal field theory using a natural Poissonian cloud of overlapping
Brownian loops, the Brownian loop-soup. In this context, the central
charge of the model is just the density of Brownian loops, SLE curves
appear as boundaries of clusters of Brownian loops, and the operators
(that should correspond to the scaling limit of local observables)
correspond to some conditioning type operators.
In the first talk, we will recall some relevant facts from joint work
with Greg Lawler and Oded Schramm concerning conformal restriction, the
relation between Brownian loops and critical percolation clusters, and
the way SLE curves get distorted when one changes the domain they are
defined in.
In the second talk, I will define the Brownian loop-soup study some of
its propertie (joint work with Greg Lawler), and then make the link with
SLE and conformal field theory.
BIO:
Wendelin Werner is professor of mathematics at the university of
Paris-Sud in Orsay. Professor Werner's research interests are
Probability Theory, relation to statistical physics, partial
differential equations and complex analysis.
_______________________________________________
Theory-group mailing list
Theory-group@cs.washington.edu
http://mailman.cs.washington.edu/mailman/listinfo/theory-group
This archive was generated by hypermail 2.1.6 : Fri Feb 27 2004 - 14:04:42 PST