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 ...
COM-309: Introduction to quantum information processingInformation is processed in physical devices. In the quantum regime the concept of classical bit is replaced by the quantum bit. We introduce quantum principles, and then quantum communications, key distribution, quantum entropy, and spin dynamics. No prio ...
COM-406: Foundations of Data ScienceWe discuss a set of topics that are important for the understanding of modern data science but that are typically not taught in an introductory ML course. In particular we discuss fundamental ideas and techniques that come from probability, information the ...
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-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 dimensions. ...
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 the main mathematical consequences (CPT, spin-statistics ...
PHYS-432: Quantum field theory IIThe goal of the course is to introduce relativistic quantum field theory as the conceptual and mathematical framework describing fundamental interactions such as Quantum Electrodynamics. ...
MICRO-310(b): Signals and systems I (for SV)Présentation des concepts et des outils de base pour l'analyse et la caractérisation des signaux, la conception de systèmes de traitement et la modélisation linéaire de systèmes pour les étudiants en sciences de la vie. Application de ces techniques au tra ...
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 see the interplay between nonparametrics and multivariate ...
MATH-561: Spectral theoryThis course is an introduction to the spectral theory of linear operators acting in Hilbert spaces. The main goal is the spectral decomposition of unbounded selfadjoint operators. We will also give elementary applications to quantum mechanics. ...
PHYS-641: Quantum ComputingAfter introducing the foundations of classical and quantum information theory, and quantum measurement, the course will address the theory and practice of digital quantum computing, covering fundamental and advanced topics such as recent quantum algorithms ...
PHYS-744: Advanced Topics in Quantum Sciences and TechnologiesThis course provides an in-depth treatment of the latest experimental and theoretical topics in quantum sciences and technologies, including for example quantum sensing, quantum optics, cold atoms, theory of quantum measurements and open dissipative quantu ...
MATH-605: Conformal bootstrap and Liouville conformal fieldThe course will focus on a probabilistic construction of a conformal field theory related to random Riemann surfaces, called the Liouville conformal field theory. The symmetries of the theory allow to express the n-point correlation functions in terms of 3 ...
