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 ...
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 ...
Concepts de base de l'analyse fonctionnelle linéaire: opérateurs bornés, opérateurs compacts, théorie spectrale pour les opérateurs symétriques et compacts, le théorème de Hahn-Banach, les théorèmes de l'application ouverte et du graphe fermé. ...
This course will serve as a first introduction to the geometry of Riemannian manifolds, which form an indispensible tool in the modern fields of differential geometry, analysis and theoretical physics. ...
La géométrie riemannienne est un (peut-être le) chapitre central de la géométrie différentielle et de la géométriec ontemporaine en général. Le sujet est très riche et ce cours est une modeste introduction aux bases du sujet. ...
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 ...
This course serves as an introduction to classical differential geometry, which studies the geometric properties of curves and surfaces in the Euclidean space. ...
This course is the basic introduction to modern cosmology. It introduces students to the main concepts and formalism of cosmology, the observational status of Hot Big Bang theory
and discusses major physical processes in the early Universe. ...
The goal of this course is to introduce the student to the basic notion of analysis on metric (measure) spaces, quasiconformal mappings, potential theory on metric spaces, etc. The subjects covered will vary each year. ...
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 ...