Quantum Topology Courses and Certifications

QuantumTopology

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
• On-Demand
• Free Video

Harvard CMSA

Abelianization in Quantum Topology

Delve into advanced mathematical concepts exploring abelianization's role in quantum topology, including Chern-Simons invariants, skein algebras, and conformal blocks in this theoretical lecture.

• YouTube
• 1 hour 1 minute
• On-Demand
• Free Video

BIMSA

Quantum Topology and Hyperbolic Geometry

Explore the fascinating intersection of quantum topology and hyperbolic geometry through advanced mathematical concepts and their interconnected relationships.

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

Centre for Quantum Technologies

Topology in Time-Evolving Quantum Systems

Delve into quantum topology's dynamic nature, exploring how symmetry changes affect topological invariants in non-equilibrium systems through experimental studies with ultracold atomic BEC in 1D lattices.

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

QuantumTopology

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

QuantumTopology

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

QuantumTopology

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

QuantumTopology

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

QuantumTopology

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

QuantumTopology

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
• On-Demand
• Free Video

QuantumTopology

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
• On-Demand
• Free Video

QuantumTopology

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
• On-Demand
• Free Video

QuantumTopology

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
• On-Demand
• Free Video

QuantumTopology

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
• On-Demand
• Free Video

QuantumTopology

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
• On-Demand
• Free Video