Fundamental Groups

Related lectures (58)

Explores the Rockafellar Theorem in optimal transport, focusing on c-cyclical monotonicity and convex functions.

Covers the concept of connected components in linear algebraic groups and their relationship to singular groups.

Covers the preliminaries in measure theory, including loc comp, separable, complete metric space, and tightness concepts.

Covers convergence theorems and integrable functions, including the Lebesgue integral and Borel-Cantelli sets.

Explores the concept of diagonalizable groups and their properties in linear algebraic groups.

Explores free abelian groups, homomorphisms, and exact sequences in the context of different categories.

Covers fundamental topics in calculus of variations, including minimizers and the Euler-Lagrange equation.

Discusses complex integration and Cauchy's theorem, focusing on integrals along curves in the complex plane.

Introduces the course on homotopical algebra, exploring the power of analogy in pure mathematics.

Explores homomorphisms, isomorphisms, group properties, and their applications through examples and exercises.

Presents the classification of finite abelian groups as products of cyclic groups, a fundamental result in various branches of mathematics.

Explores Cheeger's inequality and its implications in graph theory.

Explores distribution and interpolation spaces, showcasing their importance in mathematical analysis and the computations involved.

Covers the basics of Coq, focusing on arithmetic expressions, evaluation, and proof techniques.

Covers the long exact sequence of relative homology groups and chain complexes.

Covers the Hadamard factorisation theorem for entire functions of order at most 1.

Covers the properties and convolution of the Fourier transform.

Explores free abelian groups, homomorphisms, and exact sequences in group theory.

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