Wolff Memorial Lectures

There has been tremendous progress in the mathematical study of two-dimensional statistical mechanics models at criticality in the last 25 years. This was catalyzed by Schramm's 1999 discovery of the Schramm-Loewner evolution (SLE), which is the canonical model for a random conformally invariant non-crossing planar curve. In this talk, I will describe the origins of SLE in Loewner's 1920s work on the Bieberbach conjecture and its application in the resolution of a number of physics predictions from the 1970s-1990s about the large scale behavior of two-dimensional critical models.