Lectures related to Group Actions: Examples and Applications

Provides a recap of group theory, defining a group as a set with a multiplication operation.

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

Covers normal subgroups, quotient groups, homomorphisms, and the categorical viewpoint in group theory.

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

Explores group morphisms, kernels, and injectivity in group theory.

Covers proper actions of groups on Riemann surfaces and introduces algebraic curves via square roots.

Covers the construction and universal properties of pushouts in group theory.

Explores group actions on sets, orbits, fixed points, and classic results.

Introduces group theory basics and group action concepts with associated subsets.

Explores fundamental groups, homotopy classes, and coverings in connected manifolds.