Schramm-Loewner Evolutions Autumn 2021

Wendelin Werner
Matthis Lehmkuehler
Practical organisation

The plan is that lectures will take place live, with blackboard, on Wednesday mornings, 8:15 - 10:00 in HG G 19.1.

The lectures will also be livestreamed here. and should be then also available shortly thereafter via here.

The viewing is password protected and will be accessible only to the enrolled students.

Exercise sheets

Two of the Wednesday mornings (03/11/21 and 22/12/21) will be devoted to exercise classes - information about this will be given in due course. On these days there will therefore be an exercise class instead of a lecture. Solutions to the exercise sheets can be submitted to Matthis Lehmkuehler via email by the Monday before the exercise class (i.e. 01/11/21 and 20/12/21, respectively) by 5 p.m.

Exercise sheet Solution
Exercise sheet 1 Solution 1
Exercise sheet 2 Solution 2

Basic knowledge of Brownian motion and stochastic calculus (Ito's formula etc), basic knwoledge of complex analysis (Riemann's mapping theorem etc)

Students should however be aware that this is an advanced course, that is structured differently than a more foundational masters course (here the focus will be on the main ideas, and some proofs will only be outlined (and students are free to work out or read the details on their own).

General references on Brownian motion and stochastic calculus:

Brownian Motion, Martingales, and Stochastic Calculus by J. - F. Le Gall (Springer, 2016)

Brownian Motion and Stochastic Calculus by I. Karatzas, S. Shreve (Springer, 1998)

My own 2021 lecture notes on Brownian motion and stochastic calculus (the password will be communicated via email):

Lecture notes Part 1

Lecture notes Part 2

Links to existing lecture notes.

Here are some of the notes on SLE that can be found on the web:

My own not so recent St-Flour notes: here

Notes by Vincent Beffara: here

Notes from a course by Jason Miller here

Notes from a 2016 course by James Norris and Nathanael Berestycki here

There is also the more detailed and complete book by Grag Lawler, 'Conformally invariant processes in the plane' published by the AMS. (It contains for instance a proof of the continuity of the trace of SLE, that we will also discuss in the lectures and that is not provided in the previous lecture notes)