Lie Theory Courses and Certifications

Instituto de Matemática Pura e Aplicada

Introdução às Álgebras de Lie - Aula 20

Explore conceitos avançados de Álgebras de Lie em uma aula de doutorado ministrada por Jethro Van Ekeren, aprofundando o conhecimento em matemática pura.

• YouTube
• 1 hour 17 minutes
• Self-Paced
• Free Video

Instituto de Matemática Pura e Aplicada

Introdução às Álgebras de Lie - Aula 19

Explore conceitos avançados de Álgebras de Lie em nível de doutorado, aprofundando-se na teoria matemática com o Professor Jethro Van Ekeren.

• YouTube
• 1 hour 20 minutes
• Self-Paced
• Free Video

Instituto de Matemática Pura e Aplicada

Introdução às Álgebras de Lie - Aula 18

Explore conceitos avançados de Álgebras de Lie em nível de doutorado, aprofundando-se na teoria matemática e suas aplicações.

• YouTube
• 1 hour 31 minutes
• Self-Paced
• Free Video

Instituto de Matemática Pura e Aplicada

Introdução às Álgebras de Lie - Aula 17

Explore conceitos avançados de Álgebras de Lie em nível de doutorado, aprofundando-se na teoria matemática com o Professor Jethro Van Ekeren.

• YouTube
• 1 hour 28 minutes
• Self-Paced
• Free Video

Institut des Hautes Etudes Scientifiques (IHES)

An Introduction to Geometry and Dynamics on Semisimple Lie Groups - Lecture 3

Explore semisimple Lie groups, their structure, discrete subgroups, and asymptotic behavior through advanced mathematical concepts and theorems.

• YouTube
• 1 hour 9 minutes
• Self-Paced
• Free Video

Hausdorff Center for Mathematics

Representation Theory for Groups of Lie Type I

Explore representation theory for finite groups of Lie type, covering structural properties, Harish-Chandra theory, and Deligne-Lusztig theory for classifying irreducible complex representations.

• YouTube
• 52 minutes
• Self-Paced
• Free Video

BunG Seminar

Representation Theory of Affine Lie Algebras - Talk 22

Delve into advanced representation theory of affine Lie algebras, exploring central characters, Harish-Chandra homomorphism, Segal-Sugawara operators, and vertex operator algebras at critical level.

• YouTube
• 1 hour 43 minutes
• Self-Paced
• Free Video

IISc Bangalore;  NPTEL

An Introduction to Smooth Manifolds

Explore smooth manifold theory, from topology basics to Stokes' theorem. Covers differentiable manifolds, Lie groups, tangent spaces, and integration, ideal for advanced math and science students.

• Swayam
• 12 weeks
• Self-Paced
• Free Online Course

ICTP Mathematics

Differential Geometry

Master differential geometry through comprehensive lectures covering manifolds, curvature, and geometric structures in this ICTP diploma program by Claudio Arezzo.

• YouTube
• 1 day 2 hours 13 minutes
• Self-Paced
• Free Video

IPhT-TV

Group Theory in a Nutshell for Physicists

Master group theory fundamentals through Anthony Zee's comprehensive physics-focused approach across five detailed sessions.

• YouTube
• 9 hours 6 minutes
• Self-Paced
• Free Video

IAS | PCMI Park City Mathematics Institute

Introduction to Gauge Theory

Dive into gauge theory fundamentals through comprehensive mathematical lectures covering connections, curvature, and applications in modern geometry and physics.

• YouTube
• 4 hours 46 minutes
• Self-Paced
• Free Video

Institute for Pure & Applied Mathematics (IPAM)

Symmetric Tensor Categories and Representation Theory

Explore advanced symmetric tensor categories and their applications in representation theory, Lie superalgebras, and algebraic structures through expert lectures and collaborative research.

• YouTube
• 20 hours 55 minutes
• Self-Paced
• Free Video

ICTP Mathematics

Geometry of Moduli Spaces of Curves

Explore advanced algebraic geometry through moduli spaces of stable curves, vector bundles of coinvariants, conformal blocks, and their cohomological properties and relationships.

• YouTube
• 10 hours 34 minutes
• Self-Paced
• Free Video

NPTEL;  IISc Bangalore

An Introduction to Smooth Manifolds

The course will start with a brief outline of the prerequisites from topology and multi-variable calculus. After that a large class of examples, including Lie groups, will be presented. The course will culminate with proof of Stokes' theorem on manifolds.

• YouTube
• 1 day 11 hours
• Self-Paced
• Free Video

Mathemaniac

Demystifying Spin 1/2 - Math of Quantum Mechanics

Explore the mathematics behind spin 1/2 particles, debunking common misconceptions and providing a clear, visual explanation using the Bloch sphere representation of quantum states.

• YouTube
• 34 minutes
• Self-Paced
• Free Video