Lectures related to Further Directions: Algebraic Groups

Introduces characters as group homomorphisms from linear algebraic groups to multiplicative groups.

Explores the Monster group, a sporadic simple group with a unique representation theory.

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

Covers bijections between automorphisms and equivariant bijections in group isomorphisms.

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

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

Covers the properties of commutative linear algebraic groups and their elements.

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

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