Fredrik Johansson Viklund: Some Path Properties of the Schramm-Loewner evolution

The Schramm-Loewner evolution (SLE) is a family of random fractal curves constructed by solving the Loewner equation with a scaled Brownian motion as driving function. This talk is intended as an introduction to SLE theory for non-specialists and one aim is to give a flavor of its characteristic interplay between complex analysis and probability.

We will start by indicating how SLE curves arise naturally as fine-mesh scaling limits of interfaces in certain discrete models from statistical physics. We then survey and discuss some properties of SLE curves: the so-called phases, fractal dimension, different parameterizations, and, time permitting, multifractal spectra. We will focus especially on how to estimate the almost sure regularity of the curve in the capacity parameterization. Part of the talk is based on joint work with Greg Lawler (University of Chicago).