QuantumTopology Courses

Modified Traces on Quantum SL(2) and Logarithmic Invariants

Explore quantum sl(2), modified traces, and logarithmic invariants in this advanced topology lecture, covering key concepts and their applications in quantum mathematics.

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

On Knot Theoretical Counterpart of the Groups G^k_n

Explore knot theory's connection to groups G^k_n, covering tetrahedron relations, permutations, and invariants. Gain insights into geometry, topology, and group theory applications.

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

Quantum Cluster Algebras and Character Varieties of SL-2, R-Monodromy Problem

Explore quantum cluster algebras, character varieties, and SL(2,R)-monodromy problems through shear coordinates, local kernels, and quantum flips on Riemann surfaces.

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

Splitting Numbers and Signatures

Explore number theory and topology with a focus on splitting numbers, linking number bounds, and signature results in this advanced mathematical lecture.

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

Picture Valued Invariants, Groups, and Applications of Virtual Knot Theory

Explore picture valued invariants, groups, and applications of virtual knot theory with Professor Vassily Manturov in this advanced mathematics lecture.

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

On Complexity of Virtual Manifolds

Explore virtual manifolds' complexity, focusing on theoretical aspects and mathematical implications in quantum topology research.

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

Dijkgraaf-Witten Invariants Over Z2 for Twice Orientable Seifert Manifolds

Explore Dijkgraaf-Witten invariants over Z2 for twice orientable Seifert manifolds, delving into advanced concepts in quantum topology and manifold theory.

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

Matching Groups and Gliding Systems

Explore matching groups and gliding systems in topology, delving into advanced mathematical concepts and their applications in quantum mechanics and related fields.

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

The Stat-Sums on the Spines of Three-Dimensional Manifolds

Explore state-sums on spines of 3D manifolds with V. Turaev, delving into advanced concepts in quantum topology and geometric structures.

• YouTube
• 1 hour 38 minutes
• On-Demand
• Free Video

V. Tarkaev - The Complexity of an Infinite Series of Knots in the Thickened Torus

Explore the intricacies of knot theory as V. Tarkaev delves into the complexity of infinite knot series within a thickened torus, offering insights into advanced topological concepts.

• YouTube
• 1 hour 26 minutes
• On-Demand
• Free Video

V. Turaev - Knotoids

Explore knotoids, a mathematical concept in knot theory, with Professor V. Turaev. Delve into the intricacies of these topological structures and their applications in various fields of mathematics.

• YouTube
• 1 hour 28 minutes
• On-Demand
• Free Video

Complexity of Virtual Manifolds

Explore the intricacies of virtual manifolds and their complexity in this in-depth lecture by E. Fominykh, delving into advanced concepts in quantum topology.

• YouTube
• 1 hour 28 minutes
• On-Demand
• Free Video

When Double-Orientable Seifert Manifold Contains an Odd Surface?

Explore conditions for odd surfaces in double-orientable Seifert manifolds, delving into topological properties and mathematical implications of these unique structures.

• YouTube
• 1 hour 17 minutes
• On-Demand
• Free Video

A. Akimova - Classification of Prime Virtual Knots of Genus 1 With Low Complexity

Classification methods for prime virtual knots of genus 1, focusing on those with low complexity. Explores advanced concepts in knot theory and topology.

• YouTube
• 1 hour 21 minutes
• On-Demand
• Free Video

The Basics of TQFT

Explore the fundamental principles of Topological Quantum Field Theory (TQFT) in this comprehensive lecture, covering key concepts and applications in quantum topology.

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