MATH-225

On étudie des notions de topologie générale: unions et quotients d'espaces topologiques; on approfon ...

This course is an introduction to the theory of Riemann surfaces. Riemann surfaces naturally appear ...

This course serves as an introduction to classical differential geometry, which studies the geometri ...

The goal of this course is to give an introduction to the theory of distributions and cover the fund ...

L'objectif du cours est d'introduire les notions de base de l'algèbre linéaire et ses applications. ...

Singular cohomology is defined by dualizing the singular chain complex for spaces. We will study its ...

This course will provide an introduction to model category theory, which is an abstract framework fo ...

Discrete mathematics is a discipline with applications to almost all areas of study. It provides a s ...

Étudier les concepts fondamentaux d'analyse et le calcul différentiel et intégral des fonctions réel ...

We develop, analyze and implement numerical algorithms to solve optimization problems of the form mi ...

Homology is one of the most important tools to study topological spaces and it plays an important ro ...

Étudier les concepts fondamentaux d'analyse et le calcul différentiel et intégral des fonctions réel ...

The goal of the course is to introduce relativistic quantum field theory as the conceptual and mathe ...

The first part is devoted to Monge and Kantorovitch problems, discussing the existence and the prope ...

P-adic numbers are a number theoretic analogue of the real numbers, which interpolate between arithm ...

Calcul différentiel et intégral. Eléments d'analyse complexe. ...

Professor, working on geometry, topology, algebra

Professor, working on topology, algebra

In mathematics, topology (from the Greek words τόπος, and λόγος) is concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling, and bending; that is, without closing holes, opening holes, tearing, gluing, or passing through itself.

In the mathematical field of algebraic topology, the fundamental group of a topological space is the group of the equivalence classes under homotopy of the loops contained in the space.

In mathematics, specifically general topology, compactness is a property that seeks to generalize the notion of a closed and bounded subset of Euclidean space.

In mathematics, general topology (or point set topology) is the branch of topology that deals with the basic set-theoretic definitions and constructions used in topology.

In topology and related areas of mathematics, the quotient space of a topological space under a given equivalence relation is a new topological space constructed by endowing the quotient set of the original topological space with the quotient topology, that is, with the finest topology that makes continuous the canonical projection map (the function that maps points to their equivalence classes).

In mathematics, an order topology is a certain topology that can be defined on any totally ordered set.

In general topology and related areas of mathematics, the final topology (or coinduced, strong, colimit, or inductive topology) on a set with respect to a family of functions from topological spaces into is the finest topology on that makes all those functions continuous.

In mathematics, weak topology is an alternative term for certain initial topologies, often on topological vector spaces or spaces of linear operators, for instance on a Hilbert space.

In general topology and related areas of mathematics, the initial topology (or induced topology or weak topology or limit topology or projective topology) on a set with respect to a family of functions on is the coarsest topology on that makes those functions continuous.

In topology, a branch of mathematics, two continuous functions from one topological space to another are called homotopic (from ὁμός "same, similar" and τόπος "place") if one can be "continuously deformed" into the other, such a deformation being called a homotopy (həˈmɒtəpiː, ; ˈhoʊmoʊˌtoʊpiː, ) between the two functions.

In topology and related areas of mathematics, a product space is the Cartesian product of a family of topological spaces equipped with a natural topology called the product topology.

In topology and related areas of mathematics, a subspace of a topological space X is a subset S of X which is equipped with a topology induced from that of X called the subspace topology (or the relative topology, or the induced topology, or the trace topology).

In mathematics, a topological space is, roughly speaking, a geometrical space in which closeness is defined but cannot necessarily be measured by a numeric distance.

In functional analysis and related areas of mathematics, Fréchet spaces, named after Maurice Fréchet, are special topological vector spaces.

In mathematics, a group action on a space is a group homomorphism of a given group into the group of transformations of the space.

In the part of mathematics referred to as topology, a surface is a two-dimensional manifold.

Lecture about quotient spaces, generators and combinatorial groups.

Lecture about cell decomposition, homeomorphism and plan projective.

Lecture about fundamental groups, homotopy classes and coverings.

Lecture about group actions, discontinuous and mathematical concepts.

Lecture about topology, compactness and continuity.

Lecture about topological group, compactness and separation.

Lecture about topology, quotient spaces and open sets.

Lecture about riemann surfaces, topology and orientation.