QuantumTopology Courses

Kashaev Invariant for n-Manifolds

Explore the Kashaev invariant for n-manifolds, delving into its mathematical properties and applications in quantum topology.

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

On the Complexity of Non-Orientable Seifert Manifolds

Explore the intricacies of non-orientable Seifert manifolds and their complexity in this advanced topology lecture by M. Mulazzani.

• YouTube
• 1 hour 26 minutes
• Self-Paced
• Free Video

On Representations of Virtual Braid Group and Groups of Virtual Links

Explore representations of virtual braid groups and virtual link groups, delving into their properties, structures, and connections to quantum topology.

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

Stable Maps and Branched Shadows of 3-Manifolds

Explore stable maps and branched shadows in 3-manifolds, delving into advanced concepts in quantum topology and geometric structures.

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

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