Lectures related to Coxeter groups: Generators, Relations, and Word Length

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 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.

Coxeter Groups: Elements, Numbers, and Planes

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

Concept of Proof in Mathematics

Delves into the concept of proof in mathematics, emphasizing the importance of evidence and logical reasoning.

Coxeter Groups: Generators and Relations

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

Coxeter Groups: Reflections and Fundamental Regions

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

Cartesian Product and Induction

Introduces Cartesian product and induction for proofs using integers and sets.

Proofs: Logic, Mathematics & Algorithms

Explores proof concepts, techniques, and applications in logic, mathematics, and algorithms.

Fundamental Groups

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

Coxeter Groups: Classification and Fundamental Regions

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

Coxeter groups: classification and crystallographic construction

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

Eigenvalues of Coxeter Elements

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

The Languages of Isabelle: Isar, ML, and Scala

Explores the languages of Isabelle, focusing on Isar, ML, and Scala, covering proof schemes, Natural Deduction rules, inductive definitions, and the LCF approach.

Coxeter Groups: Classification Theorem & Order of F_4

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

Optimal Transport: Theory and Applications

Explores the theory of optimal transport, focusing on Lipschitz functions and uniqueness of solutions.

Compression: Kraft Inequality

Explains compression and Kraft inequality in codes and sequences.

Fourier Inversion Formula

Covers the Fourier inversion formula, exploring its mathematical concepts and applications, emphasizing the importance of understanding the sign.

Numerical Methods: Runge-Kutta Approximation

Covers the Runge-Kutta method for approximating solutions of differential equations.

McKay Graphs of Finite Subgroups of SU(2)

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