Lectures related to Coxeter groups: classification and crystallographic construction

Coxeter Groups: Elements, Numbers, and Planes

Explores Coxeter elements, numbers, and planes in Coxeter groups with illustrative examples.

Explores eigenvalues of Coxeter elements, cyclic permutations, invariance, and decomposition of eigenspaces.

Coxeter Groups: Reflections and Fundamental Regions

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

Coxeter Groups: Classification and Exceptional Construction

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

Coxeter Groups: Classification and Fundamental Regions

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

Coxeter groups: Generators, Relations, and Word Length

Explores Coxeter groups, word length, simple reflections, and unique elements.

McKay Graphs of Finite Subgroups of SU(2)

Explores McKay graphs for finite subgroups of SU(2) and the corresponding Coxeter graphs.

Coxeter Groups: Classification Theorem & Order of F_4

Explores the classification theorem for Coxeter groups and the order of F_4.

Coxeter Groups: Generators and Relations

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

Lee-Yang Theory

Explores the Lee-Yang theory, covering connected graphs, paths, phase diagrams, and analytic continuation.

Positive Definite Coxeter Graphs

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

Construction of Irreducible Coxeter Groups

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

Crystallographic Coxeter Groups

Explores crystallographic Coxeter groups, lattice preservation, and the classification of irreducible Weyl groups.

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.

Graph Theory Basics

Introduces induced flows, basis matrices, and tree solutions in graph theory.

Spanning Trees: Definition and Applications

Introduces spanning trees in graphs and the Minimum Spanning Tree problem, exploring efficient algorithms for optimal decision-making.

Graph Theory Fundamentals

Covers the fundamentals of graph theory, including vertices, edges, degrees, walks, connected graphs, cycles, and trees, with a focus on the number of edges in a tree.

Coxeter Groups: Simple Roots and Reflections

Explores the properties of simple roots and reflections in Coxeter groups, emphasizing uniqueness and linear independence.

Coxeter groups: reflections, rotations

Reviews Coxeter groups, reflections, rotations, and fundamental regions in finite orthogonal transformations.

Coxeter Groups: Root System Classification and Fundamental Regions

Explains root system classification and fundamental regions in Coxeter groups.