Lectures related to Positive Definite Coxeter Graphs

Coxeter groups: Generators, Relations, and Word Length

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

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.

Explores Bourgain's theorem on sparsest cut in graphs, emphasizing semimetrics and cut optimization.

Covers the proof of the Bourgain's ARV Theorem, focusing on the finite set of points in a semi-metric space and the application of the ARV algorithm to find the sparsest cut in a graph.

Coxeter Groups: Classification and Fundamental Regions

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

Coxeter Groups: Reflections and Fundamental Regions

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

McKay Graphs of Finite Subgroups of SU(2)

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

Approximation Algorithms

Covers approximation algorithms for optimization problems, LP relaxation, and randomized rounding techniques.

Sparsest Cut: Leighton-Rao Algorithm

Covers the Leighton-Rao algorithm for finding the sparsest cut in a graph, focusing on its steps and theoretical foundations.

Coxeter Groups: Elements, Numbers, and Planes

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

Construction of Irreducible Coxeter Groups

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

Coxeter groups: classification and crystallographic construction

Covers the classification of Coxeter groups, crystallographic construction, and Coxeter elements.

Coxeter Groups: Classification and Exceptional Construction

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

Automorphism groups: Trees and Graphs

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

Crystallographic Coxeter Groups

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

Eigenvalues of Coxeter Elements

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

Fourier Series: Understanding Coefficients and Periodicity

Explores Fourier series coefficients, periodicity, and series relations.

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.

Spectral Graph Theory: Introduction

Introduces Spectral Graph Theory, exploring eigenvalues and eigenvectors' role in graph properties.