Lectures related to Group Actions on Varieties

Automorphism Groups: Trees and Graphs III

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

Introduces affine varieties and covers morphisms between them and their coordinate rings.

Explores automorphisms of projective varieties, discussing isomorphism between complements and key observations on dimensions and examples.

Fixed points, orbits, and stabilizers

Covers fixed points, orbits, and stabilizers in G-varieties, including properties of closed subgroups and faithful actions.

Affine varieties: additional observations

Covers coordinate rings, closed embeddings, and operations on affine varieties.

Groupes résolubles

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

G-modules and G-varieties

Explores the embedding of chi-varieties into vector spaces with linear actions.

Modern Algebraic Geometry

Covers modern algebraic geometry, including algebraic sets, morphisms, and projective algebraic sets.

Automorphism groups of trees and graphs

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

Construction of Free Action Functor

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

Homomorphisms: Birational Maps and Affine Varieties

Covers homomorphisms between affine varieties, birational maps, regular groups, and connectedness.

Varieties with nef anti-canonical: Surjective Albanese

Presents a proof that smooth projective varieties with nef anti-canonical divisor have surjective Albanese morphism.

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

Algebraic Varieties and Morphisms

Introduces projective, quasi-projective, and algebraic varieties, emphasizing the importance of regular functions in defining morphisms.

Projective Varieties: Invariants and Dimensions

Covers invariants and dimensions of projective varieties, emphasizing their importance.

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 Actions: G-objects in a Concrete Category

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

Automorphism groups: Trees and Graphs

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

Complex Manifolds: GAGA Principle

Covers the GAGA principle, stating that any morphism on projective varieties is constant.