Lie Theory Courses and Certifications

Lie Groups - The Exceptional Lie Group G2

Explore the smallest exceptional Lie Group G2 and its surprising connections to number fields, geometry, and physics through advanced mathematical theory.

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

Lie Groups - Introduction to Lie Groups

Discover Lie Groups through examples in this Oxford undergraduate lecture, exploring their applications in analysis, geometry, and physics from foundational concepts.

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

International Centre for Theoretical Sciences

Pseudo-Reductive Groups by Brian Conrad

Explore pseudo-reductive groups with Brian Conrad, covering definitions, properties, and key theorems in this advanced mathematics lecture on algebraic group theory.

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

Insights into Mathematics

The Pentagon and Numbers Games - A Dualization of the Mutation Game

Explore the duality between the Pentagon Game and Numbers Game, examining their connections to graph dynamics and mathematical structures like ADE graphs and weight lattices.

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

Insights into Mathematics

Central Polynumber Algebra and Baby Weyl Character Formula - Math Foundations 236

Explores central polynumber algebra and Weyl character formula, focusing on SU(2) and SU(3) representations. Connects to particle physics and quaternions, emphasizing polynumbers over complex exponentials.

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

Insights into Mathematics

Central Polynumbers and SL(2)/SU(2) Characters - Math Foundations 235

Explore a novel algebraic approach to SL(2) and SU(2) representation theory, emphasizing central polynumbers and mset arithmetic, with implications for Lie theory and modern physics.

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

Insights into Mathematics

The Ubiquity of ADE Graphs, and the Mutation and Numbers Games - Math Seminars

Explore ADE graphs' mathematical significance, mutation games, and connections to advanced fields like Lie algebra, root systems, and physics in this insightful seminar on combinatorial structures.

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

Georgia Tech Research

In Search of Invariance in Brains and Machines

Explore mathematical frameworks for robust AI perception, focusing on Lie theory to model hierarchical structures and transformations in real-world object recognition.

• YouTube
• 1 hour 4 minutes
• Self-Paced
• Free Video

Fields Institute

On Conjugacy of Cartan Subalgebras in Extended Affine Lie Algebras and Classification of Torsors

Explore advanced concepts in extended affine Lie algebras and torsors over Laurent polynomial rings in this mathematical lecture by Vladimir Chernousov at the Fields Institute.

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

Fields Institute

Finite-Dimensional Representations of the Queer Lie Supergroup Q-N

Explore finite-dimensional representations of Q(n), including G-modules, Qn modules, Vera's theorem, and the typical lemma in supergeometry and bracket structures.

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

International Mathematical Union

Peng Shan- On Geometrical Realization of Centers

Explore connections between algebra centers and geometric cohomology, focusing on quantum groups and affine Springer fibers in Lie theory.

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

ICTP Mathematics

Singular Chains on Lie Groups and the Cartan Relations

Explore the connection between Lie group representations and infinitesimal descriptions using Cartan relations, with applications to Chern-Weil theory and higher local systems on classifying spaces.

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

International Mathematical Union

Theta Correspondence and the Orbit Method

Exploring theta correspondence and orbit method in representation theory, focusing on implications for unitary representations of classical groups and special unipotent representations.

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

International Mathematical Union

Analysis with Simple Lie Groups and Lattices

Explore advanced mathematical concepts focusing on simple Lie groups and lattices, delving into their analytical properties and applications in modern algebra and geometry.

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

IMSA

Welded Tangles and a Topological Interpretation of the Kashiwara-Vergne Group

Explores welded tangles and foams as higher-dimensional knot theory, connecting their automorphisms to the Kashiwara-Vergne group in Lie theory and relating to knot invariants and Baker-Campbell-Hausdorff series.

• YouTube
• 1 hour 4 minutes
• Self-Paced
• Free Video