MATH-410: Riemann surfacesThis 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 ...
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-302: Functional analysis 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-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-106(e): Analysis IIÉtudier les concepts fondamentaux d'analyse et le calcul différentiel et intégral des fonctions réelles de plusieurs
variables. ...
MATH-225: Topology II - fundamental groupsOn 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 ...
PHYS-460: Nonlinear dynamics, chaos and complex systemsThe course provides students with the tools to approach the study of nonlinear systems and chaotic dynamics. Emphasis is given to concrete examples and numerical applications are carried out during the exercise sessions. ...
MATH-106(f): Analysis IIÉtudier les concepts fondamentaux d'analyse et le calcul différentiel et intégral des fonctions réelles de plusieurs
variables. ...
MATH-106(b): Analysis IIÉtudier les concepts fondamentaux d'analyse et le calcul différentiel et intégral des fonctions réelles de plusieurs
variables. ...
MATH-318: Set theorySet Theory as a foundational system for mathematics. ZF, ZFC and ZF with Atoms. Relative consistency of the Axiom of Choice, the Continuum Hypothesis, the reals as a countable union of countable sets, the existence of a countable family of pairs without a ...
MATH-301: Ordinary differential equationsCe cours donne une introduction rigoureuse au principaux thèmes de la théorie des équations différentielles ordinaires (EDO). Les EDO sont fondamentales pour l'étude des systèmes dynamiques et des équations aux dérivées partielles. Des applications dans ce ...
MATH-512: Optimization on manifoldsWe 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 ...
MATH-680: Monstrous moonshineThe monstrous moonshine is an unexpected connection between the Monster group and modular functions. In the course we will explain the statement of the conjecture and study the main ideas and concepts leading to its proof. Our final goal is to study Borc ...
MATH-495: Mathematical quantum mechanicsQuantum 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 ...
MATH-604: Some Aspects of Calculus of VariationsThe goal of this course is to present an overview on the solvability and the regularity of relevant models of physical, technological and economical systems, which may be formulated as minimization problems of suitable integral functionals. ...
