Fundamental Groups

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Related lectures (58)

Automorphism Groups: Trees and Graphs III

Explores automorphism groups of trees and graphs, including actions on trees and group homomorphisms.

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Harmonic Forms and Riemann Surfaces Log in to Mediaspace to watch this video

Explores harmonic forms on Riemann surfaces, covering uniqueness of solutions and the Riemann bilinear identity.

Universal Property of Groups Log in to Mediaspace to watch this video

Explores the universal property of groups, defining homomorphisms and exploring subgroup properties.

Schur's Lemma and Representations Log in to Mediaspace to watch this video

Explores Schur's lemma and its applications in representations of an associative algebra over an algebraically closed field.

Group Theory Basics Log in to Mediaspace to watch this video

Introduces the basics of group theory, covering definitions, examples, subgroups, and homomorphisms.

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Groups: Definitions, Properties, and Homomorphisms Log in to Mediaspace to watch this video

Introduces the basic concepts of groups, including definitions, properties, and homomorphisms, with a focus on subgroup properties and normal subgroups.

Induced Homomorphisms on Relative Homology Groups Log in to Mediaspace to watch this video

Covers induced homomorphisms on relative homology groups and their properties.

Lifting Criterion Log in to Mediaspace to watch this video

Explores the lifting criterion for maps between path-connected and locally path-connected spaces.

Representation Theory: Algebras and Homomorphisms Log in to Mediaspace to watch this video

Covers the goals and motivations of representation theory, focusing on associative algebras and homomorphisms.

Geodesics in Wasserstein Space Log in to Mediaspace to watch this video

Explores geodesics in the Wasserstein space, emphasizing constant speed geodesics and their properties.

Lagrange's Theorem: Applications and Homomorphisms Log in to Mediaspace to watch this video

Covers Lagrange's theorem, group homomorphisms, congruence classes, and normal subgroups.

Homomorphism of Groups: Signature Log in to Mediaspace to watch this video

Explores homomorphisms of groups, focusing on the signature sgn and the concept of cycles and transpositions.

Universal Covering Log in to Mediaspace to watch this video

Explores the concept of a universal cover of a topological space and the necessary conditions for a space to have one.

Groupes Isomorphes: Applications Log in to Mediaspace to watch this video

Explores isomorphic groups, bijective morphisms, and their applications in group theory.

RSA Encryption: Main Concepts Log in to Mediaspace to watch this video

Covers the main concepts behind RSA encryption and examples of homomorphisms between cyclic groups.

Morphism of Groups Log in to Mediaspace to watch this video

Covers the concept of morphism of groups, actions on sets, and automorphisms.

Monstrous Moonshine Log in to Mediaspace to watch this video

Explores Monstrous Moonshine, focusing on the 1979 discovery and its mathematical connections.

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