The Schramm-Loewner evolution (SLE) is a one-parameter family of conformally invariant random curves that appear as lattice size scaling limits of cluster interfaces and self-avoiding walks in critical 2D lattice models. SLE processes are amenable to mathematical analysis and SLE techniques (blending complex analysis, probability, PDE) provide a geometric and rigorous approach to such scaling limits.
In the talk I will give an informal introduction to SLE. Topics will include Loewner's equation, connections to lattice models, Schramm's principle, and some basic properties. Time permitting I will try to touch on connections to CFT and Gaussian fields and current open questions and directions of research.
