The first part is devoted to Monge and Kantorovitch problems, discussing the existence and the properties of the optimal plan. The second part introduces the Wasserstein distance on measures and develops applications of optimal transport to PDEs, functiona ...
This course introduces slow/fast systems and the mathematical tools used to derive effective equations governing their behaviour. Students will learn core concepts and techniques for rigorously analysing complex stochastic multi-scale systems. ...
Introduction to classical Calculus of Variations and a selection of modern techniques. The Calculus of Variations aims at showing the existence of minimisers (or critical points) of functionals that naturally appear in mathematics and physics (Dirichlet en ...
The goal of this course is to give an introduction to the theory of distributions and cover the fundamental results of Sobolev spaces including fractional spaces that appear in the interpolation theory. Those notions are central to the study of partial dif ...
Non-positive curvature is a fundamental aspect of geometry appearing in Euclidean spaces, hyperbolic spaces, trees, buildings and many more spaces. We study it with the general but powerful tool of CA ...
Quantum mechanics is one of the most successful physical theories. This course presents the mathematical formalism (functional analysis and spectral theory) that underlies quantum mechanics. It is simultaneously an introduction to mathematical physics and ...