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Concept

Topologie

Cours associés (29)

MATH-322: Differential geometry II - smooth manifolds

Smooth manifolds constitute a certain class of topological spaces which locally look like some Euclidean space R^n and on which one can do calculus. We introduce the key concepts of this subject, such as vector fields, differential forms, etc. ...

MATH-511: Number theory II.b - Modular forms

In 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. ...

DH-405: Foundations of digital humanities

This course introduces the core concepts and methodologies of Digital Humanities, integrating both theoretical and practical perspectives. Students learn to work with large-scale cultural datasets, acquiring the tools and techniques required for their proc ...

AR-114: Modélisation numérique

Le cours de Modélisation Numérique consiste à apprendre et à manipuler les fonctions de base du logiciel de conception assistée Rhinoceros 3D grâce à l'élaboration d'un modèle simple ainsi qu'à en exploiter les capacités de rendu graphique. ...

MATH-497: Topology IV.b - homotopy theory

We 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 suspensions. We study long exact sequences. We construct Eilen ...

MATH-512: Optimization on manifolds

We 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 Riemannian geometry (with a focus dictated by computational con ...

MATH-726: Working group in Topology I

The 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-726(2): Working group in Topology II

The 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 twisted K-theory ...

MATH-436: Topology V.a - Homotopical algebra

This 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 examples of model categories and their applications in ...