Hopf Algebras Courses and Certifications

Banach Center

The Ubiquity of Hopf Algebras

Explore the pervasive nature of Hopf algebras, from historical context to practical applications in algebra and beyond. Gain insights into their structure and significance.

• YouTube
• 1 hour 13 minutes
• On-Demand
• Free Video

BIMSA

Hopf Algebras of Dimension p^2 in Positive Characteristic p

Delve into advanced mathematical concepts of Hopf algebras in positive characteristic p, exploring nonsemisimple structures and their dimensional properties through recent research findings.

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

BIMSA

Constructing Modular Tensor Categories Using Hopf Algebras

Delve into advanced mathematical concepts of modular tensor categories and their construction through Hopf algebras, focusing on ribbon factorizable structures and representation theory.

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

BIMSA

Perverse Sheaves, Hopf Algebras and Induction/Restriction Formalism

Explore advanced mathematical connections between perverse sheaves, Hopf algebras, and induction/restriction methods in this specialized algebraic geometry lecture.

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

NCCR SwissMAP

Algebraic Structures of Steinberg Modules - Hopf Algebras Part 3

Explore advanced Hopf algebra structures within Steinberg modules and their connections to polylogarithms and linear group homology.

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

Institute for Advanced Study

Hopf Algebras in the Cohomology of A_g

Delve into advanced mathematical concepts exploring Hopf algebras and their role in cohomology of A_g, examining fundamental relationships in algebraic geometry and combinatorial physics.

• YouTube
• 1 hour 5 minutes
• On-Demand
• Free Video

NCCR SwissMAP

Braided Hopf Structures on Exterior Algebras and R-Matrices

Explore braided Hopf structures on exterior algebras and R-matrices in this advanced mathematical topology lecture by R. Kashaev from the University of Geneva.

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

BIMSA

Developments in Quasi-Hopf Algebras: Construction and Classification

Delve into the construction and classification of finite-dimensional quasi-Hopf algebras, exploring recent developments and research questions in quantum symmetry theory.

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

Fields Institute

Hopf Cyclic Cohomology

Explore Hopf cyclic cohomology's evolution, from deformation complexes to braided monoidal categories, covering key breakthroughs and computational aspects in this advanced mathematical field.

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

Centre International de Rencontres Mathématiques

Orders and Shuffles on Nestohedra

Explore the mathematical connections between shuffle products and orders on nestohedra faces, extending classical results from permutohedra and associahedra to broader polytope families.

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

QuantumTopology

Pachner's 3-3 Relations and Hopf Algebras

Explore Pachner's 3-3 relations and their connections to Hopf algebras in quantum topology, delving into advanced mathematical concepts and their applications.

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

Institute for Pure & Applied Mathematics (IPAM)

Weak Quasi-Hopf Algebras Associated to Verlinde Fusion Categories

Exploration of weak quasi-Hopf algebras in relation to Verlinde fusion categories, discussing unitarity, quantum groups, and potential applications to Kazhdan-Lusztig-Finkelberg theorem.

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

Institut des Hautes Etudes Scientifiques (IHES)

Algebraic Structures in Perturbative Quantum Field Theory

Explore algebraic structures in perturbative quantum field theory through expert lectures on Feynman integrals, Hopf algebras, renormalization, and mathematical physics connections.

• YouTube
• 23 hours 43 minutes
• On-Demand
• 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
• On-Demand
• Free Video

Institut des Hautes Etudes Scientifiques (IHES)

Combinatorics and Arithmetic for Physics

Explore advanced mathematical structures connecting discrete mathematics, number theory, and theoretical physics through expert lectures on combinatorics, algebra, and computation.

• YouTube
• 13 hours 13 minutes
• On-Demand
• Free Video