# Student Probability Seminar

#### SLE and Conformal Invariance

Speaker: Reza Gheissari

Location: Warren Weaver Hall 202

Date: Friday, October 31, 2014, 2 p.m.

Synopsis:

Motivated by the scaling limits of a wide range of statistical mechanics models including LERW, percolation, GFF and Ising model, Schramm in 2000 introduced Stochastic/Schramm Loewner Evolution ($$SLE_\kappa$$). We motivate and introduce chordal $$SLE_\kappa$$ and some interesting properties of its dependence on parameter $$\kappa$$. We then give flavors for the proofs of convergence of critical percolation and Ising interfaces to $$SLE_\kappa$$ due to Smirnov (2010).