Lectures related to McKay Graphs of Finite Subgroups of SU(2)

Representation Theory: Finite Subgroups of SU(2)

Explores representation theory and character theory of finite groups, including scalar product and McKay graph.

Coxeter Groups: Generators and Relations

Explores Coxeter groups, emphasizing generators, relations, and unique presentations in group theory.

Group Theory: Reducible and Irreducible Representations

Explores group theory in quantum physics, emphasizing reducible and irreducible representations, conservation laws, and group properties.

Symmetry and Group Theory

Explores chirality, group completeness, Abelian groups, conjugate classes, and isomorphic groups in symmetry and group theory.

McKay Correspondence and Coxeter Groups

Explores the McKay correspondence, Coxeter groups, and finite subgroups of SU(2) and SO(3, emphasizing odd order properties and root system constructions.

Subgroups and Cosets: Lagrange's Theorem

Explores subgroups, normal subgroups, cosets, and Lagrange's theorem in group theory, emphasizing the importance of left cosets.

Bar Construction: Homology Groups and Classifying Space

Covers the bar construction method, homology groups, classifying space, and the Hopf formula.

Group Theory Basics: Subgroups and Homomorphisms

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

Coxeter Groups: Reflections and Fundamental Regions

Explores Coxeter groups, reflections, fundamental regions, and classification by Coxeter graphs.

Coxeter Groups: Simple Reflections and Conjugacy

Explores the theorem that an element sending all simple roots to simple roots is the identity in Coxeter groups.

Local structure of totally disconnected locally compact groups I

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

Group Theory Basics

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

Coxeter Groups: Classification and Fundamental Regions

Explores Coxeter groups classification, rotation orders, fundamental regions, and geometric equivalence.

Group Presentations

Covers the concept of group presentations using generators and relations to define groups.

Abelian Groups: First Approach

Introduces the theory of abelian groups, focusing on p-abelian groups and their structure.

Subsets and subgroups associated with an action

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

Construction of Irreducible Coxeter Groups

Explores the construction of irreducible Coxeter groups and their geometric properties, focusing on classical and simply laced groups.

Representation Theory: Algebras and Homomorphisms

Covers the goals and motivations of representation theory, focusing on associative algebras and homomorphisms.

Positive Definite Coxeter Graphs

Explores the classification of positive definite connected Coxeter graphs through detailed calculations and proofs.

Coxeter Groups: Classification and Exceptional Construction

Explores the classification and construction of Coxeter groups, focusing on exceptional cases and the method of inductive construction.