Category
Topics in topology
Related courses (8)
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This 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
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On 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-436: 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
MATH-502: Distribution and interpolation spaces
The 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-506: Topology IV.b - cohomology rings
Singular 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-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 Riemann
MATH-323: Topology III - Homology
Homology 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-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 suspen