MATH-302: Analyse fonctionnelle IConcepts 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. ...
MATH-220: Topologie I - topologie généraleNous 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 ...
MATH-476: Optimal transportThe 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 ...
MATH-502: Distribution and interpolation spacesThe 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 ...
MATH-513: Metric embeddingsThe course aims to introduce the basic concepts and results on metric embeddings, or more precisely on approximate embeddings. This area has been under rapid development since the 90's and it has strong impact on algorithms for discrete optimization proble ...
MATH-514: Nonlinear Schrödinger equationsThis course is an introduction to nonlinear Schrödinger equations (NLS) and, more generally, to nonlinear dispersive equations. We will discuss local and global well-posedness, conservation laws, the existence and stability of standing wave solutions, and ...
MATH-487: Introduction to multi-scale stochastic dynamicsThis 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. ...
PHYS-428: Relativity and cosmology IIThis 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. ...
MATH-323: Topology III - HomologyHomology is one of the most important tools to study topological spaces and it plays an important role in many fields of mathematics. The aim of this course is to introduce this notion, understand its properties and learn how to compute it. There will be m ...
MATH-506: Topology IV.a - Cohomology ringsSingular cohomology is defined by dualizing the singular chain complex for spaces. We will study its basic properties, see how it acquires a multiplicative structure and becomes a graded commutative algebra. We study an algebraic version, namely group coho ...
