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 ...
On étudie des notions de topologie générale: unions et quotients d'espaces topologiques; on approfondit les notions de revêtements et de groupe fondamental,et d'attachements de cellules et on démontre le Théorème de Seifert-van Kampen. Des exemples de surf ...
This course is an introduction to the theory of Riemann surfaces. Riemann surfaces naturally appear is mathematics in many different ways: as a result of analytic continuation, as quotients of complex domains under discontinuous group actions, as algebraic ...
Nous verrons d'abord comment la notion de continuité pour des applications entre espaces euclidiens se généralise aux applications entre espaces métriques. Nous étudierons ensuite en profondeur l'axiomatisation élégante et puissante de ces notions au cadre ...
We develop, analyze and implement numerical algorithms to solve optimization problems of the form min f(x) where x is a point on a smooth manifold. To this end, we first study differential and Riemannian geometry (with a focus dictated by computational con ...
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 ...
The students learn the theory and practice of basic concepts and techniques in algorithms. The course covers mathematical induction, techniques for analyzing algorithms, elementary data structures, major algorithmic paradigms such as dynamic programming, s ...
The focus of this reading group is to delve into the concept of the "Magnitude of Metric Spaces". This approach offers an alternative approach to persistent homology to describe a metric space across varying resolutions. It can be used to estimate an intri ...