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 d
MATH-404: Functional analysis IIWe introduce locally convex vector spaces. As an example we treat the space of test functions and the space of distributions. In the second part of the course, we discuss differential calculus in Bana
MATH-451: Numerical approximation of PDEsThe course is about the derivation, theoretical analysis and implementation of the finite element method for the numerical approximation of partial differential equations in one and two space dimens
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 theor
ME-202: Mechanical systemsCe cours vise à approfondir la compréhension des lois de fonctionnement de plusieurs principes mécaniques majeurs et largement utilisés en construction de machines, en vue d'être capable d'en faire le
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 devel
MATH-203(b): Analysis IIILe cours étudie les concepts fondamentaux de l'analyse vectorielle et l'analyse de Fourier en vue de leur utilisation pour
résoudre des problèmes pluridisciplinaires d'ingénierie scientifique.
MATH-437: Calculus of variationsIntroduction 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 n
PHYS-757: Axiomatic Quantum Field TheoryPresentation of Wightman's axiomatic framework to QFT as well as to the necessary mathematical objects to their understanding (Hilbert analysis, distributions, group representations,...).
Proofs of
MATH-485: Introduction to stochastic PDEsStochastic PDEs are used to model systems that are spatially extended and include a random component. This course gives an introduction to this topic, including some general measure theory, some Gauss
MATH-478: Dispersive PDEsThis course will give an introduction to some aspects of nonlinear dispersive partial differential equations. These are time evolution problems that arise in many contexts in physics, such as quantum
MATH-487: Topics in stochastic analysisThis course offers an introduction to topics in stochastic analysis, oriented about theory of multi-scale stochastic dynamics. We shall learn the fundamental ideas, relevant techniques, and in general
MATH-511: Number theory II.a - Modular formsIn this course we will introduce core concepts of the theory of modular forms and consider several applications of this theory to combinatorics, harmonic analysis, and geometric optimization.
MATH-665: Functional Data AnalysisA rigorous introduction to the statistical analysis of random functions and associated random operators. Viewing random functions either as random Hilbert vectors or as stochastic processes, we will s
MATH-659: Topics in dispersive PDEThis course assumes familiarity with beginning graduate level real analysis, complex analysis and functional analysis, and also basic
harmonic analysis, as well as fundamental concepts from differenti
