Title: Conformal Invariance and Two-dimensional Statistical Physics
Speaker: Professor Greg Lawler
Speaker Info: Cornell University
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 explain what the previous sentence means at least in the case of three 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 models. 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.Date: Friday, January 27, 2006
This talk is for a general mathematical audience. No knowledge of statistical physics will be assumed.