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:

- A Guide to Stochastic Loewner Evolution and its Applications by W. Kager and B. Nienhuis
- Scaling limits and the Schramm-Loewner Evolution by G. F. Lawler

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 |