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
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
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
MATH-124: Geometry for architects ICe cours entend exposer les fondements de la géométrie à un triple titre :
1/ de technique mathématique essentielle au processus de conception du projet,
2/ d'objet privilégié des logiciels de concept
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 Riemann
MATH-726: Working group in Topology IThe theme of the working group varies from year to year. Examples of recent topics studied include: Galois theory of ring spectra, duality in algebra and topology, and topological algebraic geometry.
MATH-436: Homotopical algebraThis course will provide an introduction to model category theory, which is an abstract framework for generalizing homotopy theory beyond topological spaces and continuous maps. We will study numerous
MATH-726(2): Working group in Topology IIThe theme of the working group varies from year to year. Examples of recent topics studied include: Galois theory of ring spectra, duality in algebra and topology, topological algebraic geometry and t
MATH-220: Topology I - point set topologyA topological space is a space endowed with a notion of nearness. A metric space is an example of a topological space, where a distance function measures the concept of nearness. Within this abstract
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
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
PHYS-462: Quantum transport in mesoscopic systemsThis course aims to introduce the transport behaviors of micron-size systems, emphasizing learning about recent path-breaking experiments on 2D systems such as Graphene and other vad der Waala materia
MATH-497: Topology IV.b - homotopy theoryWe propose an introduction to homotopy theory for topological spaces. We define higher homotopy groups and relate them to homology groups. We introduce (co)fibration sequences, loop spaces, and suspen
MATH-506: Topology IV.b - 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 a
CS-471: Advanced multiprocessor architectureMultiprocessors are basic building blocks for all computer systems. This course covers the architecture and organization of modern multiprocessors, prevalent accelerators (e.g., GPU, TPU), and datacen
COM-502: Dynamical system theory for engineersLinear and nonlinear dynamical systems are found in all fields of science and engineering. After a short review of linear system theory, the class will explain and develop the main tools for the quali
MATH-658: Vanishing cycles and perverse sheavesThis course will explain the theory of vanishing cycles and perverse sheaves. We will see how the Hard Lefschetz theorem can be proved using perverse sheaves. If we have more time we will try to see t
MATH-645: Young Topologists Meeting Mini-CoursesWe expect these mini-courses to equip junior researchers with new tools, techniques, and perspectives for attacking a broad range of questions in their own areas of research while also inspiring stude
