Lectures related to Automorphisms of the symmetric and alternating groups

Automorphism Groups: Trees and Graphs III

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

Explores automorphisms of graphs, focusing on automorphism groups, Cayley-Abels graphs, and quasi-isometry.

Explores automorphism groups in trees and graphs, focusing on ends and types of automorphisms.

Automorphism groups of trees and graphs II

Explores the uniqueness of trees, automorphism groups, Cayley-Abels graphs, and constructing vertex-transitive subgroups with prescribed local actions.

Group Actions: G-object Notion

Explores the categorical framework for group actions, focusing on the concept of G-objects in different categories.

Group Theory: Action on a Product

Explores actions on products in group theory, including automorphism construction and preservation of products.

Group Actions: G-objects in a Concrete Category

Explores G-objects in a concrete category and the framework for group actions.

Construction of Free Action Functor

Explores the construction of the free action functor and its equivariance.

Covers self-similar groups and automorphisms of rooted trees, exploring residually finite groups and congruence subgroups.

Permutations and Symmetric Groups

Covers symmetric groups, transpositions, sign of a permutation, and conjugacy classes in permutations.

Groupes résolubles

Explores solvable groups, group actions, normalizers, and stabilizers in group theory.

Group Theory: Group Actions on Products

Covers defining group actions on products and constructing automorphisms in group theory.

Equidistribution of CM Points

Covers the joint equidistribution of CM points in algebraic structures and quadratic forms.

Group Theory Basics

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

The Weil Representation: Part 2

Covers the Weil representation, Heisenberg group actions, and symplectic group concepts.

Symmetric Group and Alternating Group

Explores the Symmetric group, cycle notation, multiplication, the sign of a permutation, and the Alternating group.

Group Morphisms and Determinants

Explores group morphisms and determinants in K-vector spaces.

Group Morphisms: Injectivity and Conjugation

Explores group morphisms, injectivity criteria, and conjugation concepts within groups.

Properties of Sylow Subgroups

Covers the second and third properties of p-Sylow subgroups and their automorphisms.

Group Actions on Varieties

Explores group actions on varieties, including orbits, stabilizers, and G-invariant morphisms.