QuantumTopology Courses

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

R. Kashaev - The Connection Between Integrals and Fourier Series

Explore the intricate relationship between integrals and Fourier series, delving into mathematical concepts that bridge these fundamental analytical tools in advanced calculus and mathematical physics.

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

S. Matveev - Dijgraaf-Witten Invariants for Seifert Manifolds

Explore Dijgraaf-Witten invariants for Seifert manifolds in this advanced topology lecture, delving into complex mathematical concepts and their applications in quantum theory.

• YouTube
• 1 hour 35 minutes
• On-Demand
• Free Video

V. Tarkaev - Construction of the Khovanov Homology

Explore the construction of Khovanov homology, a powerful invariant in knot theory, and its applications in quantum topology and low-dimensional manifolds.

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

Tensor Calculus - Reminders

Обзор основ тензорного исчисления и его применения в физике и математике. Включает напоминания о ключевых концепциях и методах.

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

V. Tarkaev - Kahsaev Task for 4-Dimensional Manifolds

Explore Kahsaev's task for 4-dimensional manifolds in this advanced topology lecture, delving into complex mathematical concepts and their applications in quantum theory.

• YouTube
• 1 hour 34 minutes
• On-Demand
• Free Video