Teaching

IST Austria

Fall 2015/16: Selected Topics in Partial Differential Equations

Stochastic partial differential equations (SPDEs) are used to model a wide variety of physical systems subject to randomness or noise. In many interesting situations, solutions to SPDEs are very irregular, which makes their analysis particularly challenging. In the last couple of years, spectacular progress has been obtained through the use of “rough paths theory” and the development of the theory of “regularity structures”, for which M. Hairer has been awarded a Fields Medal. In this course we aim to give a gentle introduction to SPDEs with a special emphasis on these recent developments.

Literature:

More information can be found at the course website (Part I / Part II ).

Spring 2015: Optimal Transport

The Monge-Kantorovich problem of optimal transport is to transfer mass from a given initial distribution to a prescribed target distribution in such a way that the total transport costs are minimized. This problem has originally been motivated by applications in engineering and economics. In the last decades, several unexpected connections have been discovered between optimal transport and seemingly unrelated problems in analysis, probability theory and geometry.

This course presents an overview of these developments. Some of the topics that we will discuss are gradient flow methods for evolution equations, Ricci curvature bounds for metric measure spaces, functional inequalities, isoperimetry, and concentration of measure.

We shall cover parts of the following books:

More information can be found at the course website

University of Bonn

Summer 2014 Regularity Structures (reading class, master)
Summer 2014 Analysis and Probability of Boolean Functions (seminar, master)
Winter 2013 Stochastic Partial Differential Equations (lectures, master)
Summer 2012 Angewandte Stochastik (lectures, bachelor)
Summer 2011 Markov Processes (lectures, master)

TU Delft

2008 – 2009 Analysis 1 (for Mechanical Engineering)
Product in werking (Analysis for Industrial Design)
2007 – 2008 Analysis 1 (for Mechanical Engineering)
Analysis 2 (for Mechanical Engineering)
Product in werking (Analysis for Industrial Design)
2006 – 2007 Analysis 1 (for Mechanical Engineering)
2005 – 2006 Analysis 2 (for Mechanical Engineering)