This course will be an introduction to Schramm-Loewner Evolutions which are natural random planar curve that arise in a number of contexts in probability theory and statistical theory in two dimensions.

Objective

The goal of the course is to provide an overview of the definition and the main properties of Schramm-Loewner Evolutions (SLE).

Content

Most of the following items will be covered in the lectures: - Introduction to SLE - Definition of SLE - Phases of SLE, hitting probabilities - How does one prove that an SLE is actually a curve? - Restriction, locality - Relation to loop-soups and the Gaussian Free Field - Some SLEs as scaling limit of lattice models

Performance assessment

Performance assessment information (valid until the course unit is held again)