Lie Algebras Courses and Certifications

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
• On-Demand
• Free Video

QuantumTopology

Brunnian Braids and Lie Algebras

Explore the fascinating connection between Brunnian braids and Lie algebras in this advanced mathematical lecture by Vladimir Vershinin, delving into complex topological structures.

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

Institute for Advanced Study

Lie Algebras and Homotopy Theory - Jacob Lurie

Explore connections between Lie algebras and homotopy theory, covering fundamental groups, Whitehead brackets, and Quillen's theorem in this advanced mathematics seminar.

• YouTube
• 1 hour 1 minute
• On-Demand
• Free Video

Michael Penn

The Derivative Is a Lie

Explore the concept of derivatives through a whimsical narrative, blending mathematical concepts with creative storytelling to make complex ideas more accessible and engaging.

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

International Centre for Theoretical Sciences

Deformation of Representation and Fusion Rings for a Lie Algebra by Swarnava Mukhopadhyay

Explores deformation theory in representation and fusion rings of Lie algebras, discussing mathematical concepts and their applications in algebraic and combinatorial methods.

• YouTube
• 1 hour 18 minutes
• On-Demand
• Free Video

NCCR SwissMAP

The Stabilizer Lie Algebra of the Harmonic Coproduct

Explore the stabilizer Lie algebra of the harmonic coproduct, delving into algebraic and topological concepts related to the Grothendieck-Teichmüller group.

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

Institut des Hautes Etudes Scientifiques (IHES)

Inequalities Defining Polyhedral Realizations of Affine Types and Extended Young Diagrams

Explore crystal bases in Lie algebra representation theory, focusing on polyhedral realizations and explicit inequalities for classical affine types using extended Young diagrams.

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

BunG Seminar

Construction of Finite W-algebras and Slodowy Slice Quantization

Delve into advanced mathematical concepts of Slodowy slices, nilpotent orbits, and finite W-algebras, exploring their construction, Poisson structures, and quantization methods in semisimple Lie algebras.

• YouTube
• 1 hour 23 minutes
• On-Demand
• Free Video

BunG Seminar

Chiral and Factorization Algebra - Lecture 25

Delve into advanced mathematical concepts exploring chiral and factorization algebras, their equivalence, and the relationship with Lie-* algebras, culminating in the Eckmann-Hilton commutativity theorem.

• YouTube
• 1 hour 48 minutes
• On-Demand
• Free Video

University of Chicago Department of Mathematics

Poisson Algebra, Combinatorics and Representations of Surface Groups

Dive into Poisson algebras, combinatorics, and surface group representations. Explore Goldman's Lie algebra construction and its applications to character varieties and Anosov representations.

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

Galileo Galilei Institute

Mysterious Triality

Explore the enigmatic concept of triality in mathematics and physics, unraveling its connections to symmetry, algebra, and quantum mechanics.

• YouTube
• 1 hour 17 minutes
• On-Demand
• Free Video

M-Seminar, Kansas State University

Maulik-Okounkov Lie Algebras and BPS Lie Algebras

Explore the connection between Maulik-Okounkov and BPS Lie algebras, examining their roles in quiver varieties and cohomological DT theory. Gain insights into non-abelian stable envelopes and Okounkov's conjecture.

• YouTube
• 1 hour 29 minutes
• On-Demand
• Free Video

Conference GSI

TRANSVERSE POISSON STRUCTURES TO ADJOINT ORBITS IN A COMPLEX SEMI-SIMPLE LIE ALGEBRA

Explore transverse Poisson structures in complex semi-simple Lie algebras, focusing on adjoint orbits and their nilpotent cases. Discover determinantal formulas and quasihomogeneous polynomials in this advanced mathematical topic.

• YouTube
• 1 hour 4 minutes
• On-Demand
• Free Video

Centre de recherches mathématiques - CRM

Extensions of Affine Algebra Vertex Operator Algebras

Explore extensions of affine algebra VOAs, focusing on V(g,k) for simple Lie algebras. Learn about finite-index extensions, simple currents, and quantum subgroups in module category classification.

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

Centre de recherches mathématiques - CRM

Towards the Quantum Exceptional Series

Explore continuous families of planar algebras interpolating exceptional Lie algebras and their quantum counterparts. Discover a potential new exceptional knot polynomial through skein theoretic analysis.

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