Schramm-Loewner Evolution reading group

Schramm-Loewner evolution with parameter κ (SLE(κ)) describes the evolution of certain random curves in the complex plane. It plays an important role in statistical mechanics, where it has been shown to be the scaling limit of various lattice models, including the Gaussian Free Field and loop erased random walks, depending on the value of κ.

In the first half of this course, we will introduce SLE and look at some of its properties and the various phases it admits. The second half of this course will then focus on some of the discrete models whose scaling limit is an SLE. We will mainly follow the lecture notes by Nathanaël Berestycki and James Norris, which can be found here, however the following notes are also useful:

Timetable

Date/time Venue Topic Speaker
Wed 22nd Feb, 14:15 - 16:15 CB 3.9 Introduction to SLE I Emma Horton
Wed 1st March, 14:15 - 16:15 6W 1.1 Introduction to SLE II John Fernley
Wed 8th March, 14:15 - 16:15 CB 3.9 Phases of SLE Sandra Palau Calderón
Wed 15th March, 14:15 - 16:15 6W 1.1 Radial SLE John Fernley
Wed 22nd March, 14:15 - 16:15 6W 1.1 Loop-erased random walks: Notes, Paper Sam Moore
Wed 29th March, 14:15 - 16:15 CB 4.1 Percolation Cécile Mailler
Wed 5th April, 14:15 - 16:15 Wolfson Self-avoiding walks Dorottya Fekete
Wed 26th April, 14:15 - 16:15 Wolfson No lecture
Wed 3rd May, 14:15 - 16:15 Wolfson Gaussian free field Emma Horton