Lie Theory Courses and Certifications

Mathemaniac

Lie Groups, Algebras, and Brackets - Visual Introduction to Lie Theory

Discover Lie theory through visual intuition, exploring groups, algebras, rotations in higher dimensions, exponentials, matrix operations, and the geometric meaning behind abstract concepts.

• YouTube
• 2 hours 17 minutes
• On-Demand
• Free Video

Institut des Hautes Etudes Scientifiques (IHES)

Global Lie Theory: Wild Riemann Surfaces and Their Character Varieties

Explore the evolution of topological symplectic structures, wild Riemann surfaces, and character varieties in global Lie theory. Discover connections to quantum groups, hyperkähler geometry, and integrable systems.

• YouTube
• 1 hour 12 minutes
• On-Demand
• Free Video

Centre International de Rencontres Mathématiques

Higher Lie Theory in Positive Characteristic

Explore advanced concepts in Higher Lie theory for positive characteristic fields, delving into algebraic and geometric perspectives of this mathematical domain.

• YouTube
• 1 hour 3 minutes
• On-Demand
• Free Video

BIMSA

Lie Theory in Tensor Categories with Applications to Modular Representation Theory

Delve into advanced mathematical concepts of Lie theory in tensor categories and their applications to modular representation theory, focusing on decomposition theorems and algebraic number properties.

• YouTube
• 1 hour 20 minutes
• On-Demand
• Free Video

BIMSA

Canonical Bases in Lie Theory and Total Positivity

Explore canonical bases in Lie theory and their connection to total positivity through advanced mathematical insights from leading expert George Lusztig.

• YouTube
• 55 minutes
• On-Demand
• Free Video

Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Leaf Spaces in Lie Theory and Banach Manifold Quotients

Explore advanced concepts in Lie theory through quotients of Banach manifolds and regular foliations, focusing on pseudogroup actions and their applications in infinite-dimensional geometry.

• YouTube
• 58 minutes
• On-Demand
• Free Video

Fields Institute

The Lie Theory Behind Geometric Classification Problems - Relative Algebroids Part 2

Delve into advanced Lie theory applications for geometric classification through relative algebroids in this comprehensive mathematical exploration.

• YouTube
• 2 hours 9 minutes
• On-Demand
• Free Video

Fields Institute

The Lie Theory Behind Geometric Classification Problems - Relative Algebroids Part 1

Explore Lie theory applications to geometric classification through relative algebroids in this advanced mathematical lecture from the Fields Institute.

• YouTube
• 2 hours 21 minutes
• On-Demand
• Free Video

International Mathematical Union

The Formal Model of Semi-Infinite Flag Manifolds

Explore the formal model of semi-infinite flag manifolds as explicit algebro-geometric objects, examining recent developments in affine Lie algebra representation theory and discussing implications.

• YouTube
• 45 minutes
• On-Demand
• Free Video

International Mathematical Union

Evgeny Feigin - PBW Degenerations, Quiver Grassmannians, and Toric Varieties

Explore connections between Lie theory, quiver Grassmannians, and flag variety degenerations, focusing on PBW filtration in highest weight representations and its impact on degenerate flag varieties.

• YouTube
• 45 minutes
• On-Demand
• Free Video

IMSA

Fundamentals of Lie Groupoids and Algebroids - Lecture Series

Introducción a la teoría de Lie de grupoides y algebroides, explorando sus definiciones, propiedades y aplicaciones en diversas estructuras geométricas.

• YouTube
• 1 hour 3 minutes
• On-Demand
• Free Video

IMSA

Frontiers in Mathematics Lecture Series - Research Talk

Explore Lie theory, groupoids, and algebroids in this advanced mathematics seminar. Discover local integration techniques and their implications for non-integrable Lie algebroids.

• YouTube
• 51 minutes
• On-Demand
• Free Video

International Centre for Theoretical Sciences

Symmetric Closed Subsets of Real Affine Root Systems and Regular Su - Short Talk by Irfan Habib

Explores symmetric closed subsets of real affine root systems and their applications in representation theory, focusing on algebraic and combinatorial methods.

• YouTube
• 1 hour 19 minutes
• On-Demand
• Free Video

International Centre for Theoretical Sciences

From Faces of Weyl Polytopes, to Weights and Characters of Highest Weight Modules by Apoorva Khare

Explore connections between Weyl polytopes, weights, and characters in highest weight modules. Gain insights into algebraic and combinatorial methods in representation theory.

• YouTube
• 1 hour 28 minutes
• On-Demand
• Free Video

International Centre for Theoretical Sciences

Abelianizations of Lie Algebras by Dynkin Combinatorics

Explore Dynkin combinatorics to understand abelianizations of Lie algebras, delving into advanced algebraic structures and their representations in modern mathematics.

• YouTube
• 1 hour 16 minutes
• On-Demand
• Free Video