QuantumTopology Courses

Twisted Homology and Twisted Simplical Groups - Another Approach to Quantum Topology

Explore twisted homology and simplicial groups as alternative approaches to quantum topology, delving into advanced mathematical concepts and their applications.

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

Realisation of Cycles and Small Covers Over Graph Associahedra

Explore graph associahedra, focusing on realisation of cycles and small covers. Gain insights into this advanced mathematical topic through expert analysis and explanations.

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

Rectangular Diagrams and Giroux's Convex Surfaces

Explore rectangular diagrams and Giroux's convex surfaces in topology, delving into advanced mathematical concepts and their applications in quantum mechanics.

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

Jacobians of Circulant Graphs

Explore Jacobians of circulant graphs with A. D. Mednykh, delving into advanced mathematical concepts and their applications in graph theory and topology.

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

Self-Intersection of Curves in Surfaces and Drinfeld Associators

Explore self-intersection of curves in surfaces and Drinfeld associators, delving into advanced mathematical concepts and their applications in quantum topology.

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

The Thurston Norm of 3-Manifolds with a 2-Generator Fundamental Group

Explore the Thurston norm in 3-manifolds with 2-generator fundamental groups, delving into advanced concepts in quantum topology and geometric group theory.

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

Additive Posets, CW-Complexes, and Graphs

Explore additive posets, CW-complexes, and graphs in topology with renowned mathematician V.G. Turaev, delving into advanced concepts and their interconnections.

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

Homology of Jucys Murphy Elements and the Flag Hilbert Scheme

Explore the intricate connections between Jucys-Murphy elements and flag Hilbert schemes, delving into their homological properties and algebraic structures.

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

On the Hurwitz Existence Problem for Branched Covers Between Surfaces

Explore the Hurwitz existence problem for branched covers between surfaces, delving into mathematical concepts and theories related to topology and surface geometry.

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

The Spaces of Non Contractible Closed Curves in Compact Space Forms

Explore non-contractible closed curves in compact space forms, delving into advanced mathematical concepts and their applications in quantum topology.

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

Quantum Racah Matrices and Evolution of Knots

Explore quantum Racah matrices and their role in knot evolution, delving into advanced concepts in quantum topology and mathematical physics.

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

Turaev Viro Invariants and Complexity of Virtual 3-Manifolds

Explore Turaev-Viro invariants and their application in determining complexity of virtual 3-manifolds, advancing understanding in quantum topology and geometric structures.

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

The Kashaev Invariant, Nahm Sums and Modularity

Explore the Kashaev invariant, Nahm sums, and modularity in quantum topology, delving into advanced mathematical concepts and their applications.

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

On Volumes of Compact and Non-Compact Right-Angled Hyperbolic Polyhedra

Explore the mathematical intricacies of right-angled hyperbolic polyhedra, examining volume calculations for both compact and non-compact forms in this advanced geometry lecture.

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

Colored Graphs and Complements of Knots and Links

Explore 4-colored graphs and their relationship to knot and link complements, delving into topological concepts and graph theory applications in knot theory.

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