Lectures related to Group Actions: Examples and Applications

Group Actions: Theory and Examples

Explores concrete examples of group actions on sets, focusing on actions that do not change the set.

Group Theory Basics: Subgroups and Homomorphisms

Introduces subgroups and homomorphisms in group theory, with examples for illustration.

Group Theory Basics

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

Subsets and subgroups associated with an action

Explores subsets and subgroups related to group actions on sets.

Active Learning: Group Homomorphisms

Explores group homomorphisms, emphasizing surjective mappings and their impact on group questions.

Groups: Definitions, Properties, and Homomorphisms

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

Subsets and subgroups associated with an action

Explores subsets, subgroups, actions, fixed points, stabilizers, orbits, and bijections in group theory.

Push-out and Quotients

Delves into push-out and quotients in group theory, emphasizing homomorphisms and normal subgroups.

Categorical Perspective: Group Quotients

Explores the categorical sense of constructing a group quotient by a normal subgroup, showing it as a specific example of a more general construction.

Class Equation and Burnside's Lemma

Explores the class equation and Burnside's lemma in group theory.

Recap of Group Theory

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

Universal Property of Groups

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

Group Theory: Quotients of Group

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

Automorphism Groups: Trees and Graphs III

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

Groups & Rings: Morphisms, Kernels, and Injectivity

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

Proper Actions and Quotients

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

Pushouts in Group Theory: Universal Properties Explained

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

Basic Notions, Ch III: Group Actions

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

Group Theory Fundamentals

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

Fundamental Groups

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