QuantumTopology Courses

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

Knot Invariants Arising from Homological Operations on Khovanov Homology

Explore advanced knot theory through homological operations on Khovanov homology, uncovering new invariants and their applications in quantum topology.

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

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
• Self-Paced
• Free Video

Triangular Decomposition of Skein Algebras and Quantum Teichmuuller Spaces

Explore triangular decomposition of skein algebras and quantum Teichmuller spaces in this advanced mathematical lecture by Thang Le, delving into complex topological concepts.

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

Linking Numbers in Non-Orientable 3 Manifolds

Explore linking numbers in non-orientable 3-manifolds, delving into advanced topological concepts and their applications in quantum theory and mathematical physics.

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

E. Fominykh - Special Spines with Three 2-Components

Explore special spines with three 2-components in topology, focusing on their unique properties and applications in quantum theory and geometric structures.

• YouTube
• 1 hour 20 minutes
• Self-Paced
• Free Video

A. Akimova - Homologically Trivial Knots in Thickened Surfaces

Explore homologically trivial knots in thickened surfaces, examining their properties and implications for quantum topology research.

• YouTube
• 1 hour 31 minutes
• Self-Paced
• Free Video

A. Slepcov - Quantum Invariants of Knots and Their Properties

Explore quantum invariants of knots, their properties, and applications in topology. Gain insights into advanced mathematical concepts and their relevance in quantum theory.

• YouTube
• 1 hour 31 minutes
• Self-Paced
• Free Video

Conjugation of Global Knots

Explore the mathematical concept of conjugation in global knots, delving into advanced topological theories and their applications in quantum mechanics.

• YouTube
• 1 hour 8 minutes
• Self-Paced
• Free Video

Non-Orientable Seifert Manifolds

Explore non-orientable Seifert manifolds in this advanced topology lecture, delving into complex mathematical concepts and their implications in quantum topology research.

• YouTube
• 1 hour 27 minutes
• Self-Paced
• Free Video

Ph. Kirablev - Combinatorial Description of Heegaard Floer Homology

Explore combinatorial approaches to Heegaard Floer homology, a powerful invariant in low-dimensional topology, with insights from Ph. Kirablev's lecture on advanced mathematical techniques.

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

E. Fominykh - On a Series of Tetrahedral Manifolds

Explore tetrahedral manifolds in quantum topology, examining their properties and implications for mathematical research and applications in related fields.

• YouTube
• 1 hour 31 minutes
• Self-Paced
• Free Video