Lectures related to Root system

Covers Borcherds' proof strategy, emphasizing the significance of simple roots and Weyl vectors.

Delves into Macdonald identities, covering affine root systems, modular forms, and Lie algebras.

Explores Weyl characters, Macdonald's identities, and Borcherds products in Euclidean space.

Coxeter Groups: Simple Roots and Reflections

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

Coxeter Groups: Root System Classification and Fundamental Regions

Explains root system classification and fundamental regions in Coxeter groups.

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Eigenvalues of Coxeter Elements

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

Coxeter groups: reflections, rotations

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

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.

Diffusion-Convection: Modeling and Schemes

Covers modeling and numerical schemes for diffusion-convection problems.

Simple Lie Algebras: Classification and Properties

Explores the classification and properties of simple complex Lie algebras, emphasizing their connection with Lie groups.

Coordinate Systems and Applications

Covers the definition and use of coordinate systems and applications in bases and linear equations.

Central Results in Hermite Forms

Covers central results in Hermite forms and principal series representations in group theory.

Coxeter Groups: Reflections and Fundamental Regions

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

Construction of Irreducible Coxeter Groups

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

Comsol: Parallel plate capacitor

Focuses on modeling a parallel plate capacitor using Comsol, emphasizing clear project ideas and group collaboration.

Powers and Roots: Definitions and Properties

Explains the definitions and properties of powers and roots in algebra.

Crystallographic Coxeter Groups

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

Coxeter Groups: Geometric Equivalence and Positive Definite Graphs

Explores the geometric equivalence of Coxeter groups with the same graph and positive definite matrices.

Harmonic Oscillator: Damped Regimes

Explores the analysis of a harmonic oscillator under different damping regimes, focusing on strong and critical damping.