Lie Algebras Courses and Certifications

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

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

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

Fields Institute

The Lie Algebra Associated with the Lower Central Series of a Right-Angled Coxeter Group

Explore the Lie algebra's connection to lower central series in right-angled Coxeter groups, delving into advanced mathematical concepts and their implications.

• YouTube
• 29 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

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

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

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

Prague Mathematical Physics Seminar

Clifford Algebra Analogue of Cartan's Theorem for Symmetric Pairs

Discover the Clifford algebra extension of Cartan's classical theorem applied to symmetric pairs in this advanced mathematical physics seminar.

• YouTube
• 1 hour 7 minutes
• On-Demand
• Free Video

M-Seminar, Kansas State University

Quantum Algebras and Spectral R-matrices from Equivariant Affine Grassmannians - Part 1

Delve into quantum algebras and spectral R-matrices through equivariant affine Grassmannian geometry, exploring connections to holomorphic-topological twist of 4D N=2 gauge theories.

• YouTube
• 1 hour 8 minutes
• On-Demand
• Free Video

M-Seminar, Kansas State University

Quantum Algebras, Spectral R-matrices from Equivariant Affine Grassmannians - Part 2

Delve into quantum algebras and spectral R-matrices through equivariant affine Grassmannians, exploring Niu's work on quantizations of Yang's r-matrix and their connections to 4D N=2 gauge theories.

• YouTube
• 1 hour 36 minutes
• On-Demand
• Free Video

BunG Seminar

Semi-infinite Cohomology and BRST Complex in W-algebras

Delve into advanced mathematical concepts of semi-infinite cohomology, exploring W-algebras through BRST resolution and discovering connections to Tate Lie algebra and Zhu's algebra theory.

• YouTube
• 1 hour 53 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

Institut des Hautes Etudes Scientifiques (IHES)

Inequalities Defining Polyhedral Realizations and Monomial Realizations in Crystal Bases

Delve into advanced crystal bases theory, exploring polyhedral and monomial realizations in Lie algebras, with focus on inequalities defining convex cones and Laurent monomial expressions.

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