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
MATH-488: Topology IV.a -Algebraic K-theoryAlgebraic K-theory, which to any ring R associates a sequence of groups, can be viewed as a theory of linear algebra over an arbitrary ring. We will study in detail the first two of these groups and a
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-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 el
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
MATH-100(b): Advanced analysis IDans ce cours, nous étudierons les notions fondamentales de l'analyse réelle, ainsi que le calcul différentiel et intégral pour les fonctions réelles d'une variable réelle.
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
ChE-403: Heterogeneous reaction engineeringThe theoretical background and practical aspects of heterogeneous reactions including the basic knowledge of heterogeneous catalysis are introduced. The fundamentals are given to allow the design of m
MATH-684: Spectral sequencesThe goal of the course is to learn how to construct and calculate with spectral sequences. We will cover the construction and introductory computations of some common and famous spectral sequences.