Departmental Colloquium
Gregory Lawler
University of Chicago
CONFORMAL INVARIANCE AND TWO-DIMENSIONAL STATISTICAL PHYSICS
Abstract:
A number of lattice models in two-dimensional statistical
physics are conjectured to exhibit conformal invariance
in the scaling limit at criticality. In this talk, I will
try to explain what the previous sentence means, focusing on
three elementary examples: simple random walk, self-avoiding walk,
loop-erased random walk. I will describe the
limit objects,
Schramm-Loewner Evolution (SLE), the Brownian loop soup, and
the normalized partition functions, and show how conformal
invariance can be used to calculate quantities ("critical
exponents") for the model. I will also describe why (in some
sense) there is only a one-parameter family of conformally
invariant limits. In conformal field theory, this family
is parametrized by central charge.
Much of the talk will be based on joint work with Oded
Schramm and Wendelin Werner although I will discuss
work by a number of other researchers.
This talk is for a general mathematical audience. No knowledge
of statistical physics will be assumed.
Friday February 16, 2007 at 3:00 PM in SEO 636