Lectures related to Endomorphisms and automorphisms of totally disconnected locally compact groups I

Local structure of totally disconnected locally compact groups I

Covers the local structure of totally disconnected locally compact groups, exploring properties and applications.

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

Local structure of totally disconnected locally compact groups III

Explores the local structure of totally disconnected locally compact groups and their isomorphisms through conjugation.

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.

Invariant Definitions

Explores invariant definitions in sets, groups, and automorphisms, including p-divisible groups and free abelian groups.

Proper Actions and Quotients

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

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

Convergence and Compactness in R^n

Explores adhesion, convergence, closed sets, compact subsets, and examples of subsets in R^n.

Mild Dissipative Surface Dynamics

Explores mild dissipative surface dynamics, including conservative behavior and ergodic functions.

Endomorphisms and automorphisms of totally disconnected locally compact groups

Explores endomorphisms and automorphisms of totally disconnected locally compact groups, emphasizing the properties of flat groups and free abelian subgroups.

Differential Forms Integration

Covers the integration of differential forms on smooth manifolds, including the concepts of closed and exact forms.

Local structure of totally disconnected locally compact groups II

Explores the local structure of totally disconnected locally compact groups, covering commensurated subgroups, completions, local automorphisms, and the quasi-centre.

Normed Spaces

Covers normed spaces, dual spaces, Banach spaces, Hilbert spaces, weak and strong convergence, reflexive spaces, and the Hahn-Banach theorem.

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.

Modular curves: Riemann surfaces and transition maps

Covers modular curves as compact Riemann surfaces, explaining their topology, construction of holomorphic charts, and properties.

Endomorphisms and automorphisms of totally disconnected locally compact groups II

Explores flat groups of automorphisms and their properties, including minimization functions and invariance under specific conditions.

Open Mapping Theorem

Explains the Open Mapping Theorem for holomorphic maps between Riemann surfaces.

Automorphism Groups: Trees and Graphs III

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

Endomorphisms and automorphisms of totally disconnected locally compact groups III

Explores the properties of endomorphisms and automorphisms of locally compact groups, emphasizing invariance, tree representation theory, and minimal subgroups.