The Schramm-Loewner evolution (SLE) is a random fractal curve in the plane that describes the scaling limit of interfaces in several statistical physics models. It is uniquely characterized by two properties known as conformal invariance and the domain Markov property. The first two lectures of the course will be an introduction to SLE and its basic properties via classical Loewner chain theory. The third lecture will be about imaginary geometry, which gives a very useful alternative perspective on SLE.
prerequisites: The course will require no prior knowledge except standard graduate probability courses. There will be a small amount of stochastic calculus at a few occasions (e.g. I will refer to Ito's formula).