Quantum Topology Courses and Certifications

QuantumTopology

D. Ilyutko - Chord Diagrams

Explore chord diagrams in topology, their applications, and mathematical properties. Gain insights into this powerful tool for visualizing and analyzing complex relationships in data structures.

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

QuantumTopology

Ph. Korablev - Yang-Baxter Operators and Invariants of Links

Explore Yang-Baxter operators and their applications in link invariants, delving into quantum topology concepts and mathematical techniques for analyzing knot structures.

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

QuantumTopology

Simplified Khovanov Rozansky Calculus

Explore simplified Khovanov Rozansky calculus with Andrey Morozov, delving into advanced quantum topology concepts and their applications in mathematical physics.

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

QuantumTopology

On a High Dimensional Generalization of Seifert Fibrations

Explore high-dimensional generalizations of Seifert fibrations, extending classical concepts to modern topological structures and manifolds.

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

QuantumTopology

3 Dimensional HQFTs

Explore 3-dimensional Homotopy Quantum Field Theories with Alexis Virelizier, delving into advanced mathematical concepts and their applications in quantum topology.

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

QuantumTopology

Re Normalized TQFTs

Explore re-normalized Topological Quantum Field Theories with Nathan Geer, delving into advanced concepts in quantum topology and mathematical physics.

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

QuantumTopology

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

Banach Center

3D Quantum Trace Map: Construction and Applications in Ideally Triangulated 3-Manifolds

Explore the construction of the 3d quantum trace map, linking Kauffman bracket skein modules to quantum gluing modules in ideally triangulated 3-manifolds.

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

Institut des Hautes Etudes Scientifiques (IHES)

Quantum Chern-Simons Theory: Real and Complex Formulations - Lecture 3

Explore WRT invariants, Resurgence conjecture, and Teichmüller TQFT in quantum Chern-Simons theory, with detailed examples and new formulations.

• YouTube
• 1 hour 11 minutes
• On-Demand
• Free Video

Institut des Hautes Etudes Scientifiques (IHES)

Quantum Chern-Simons Theory: Real and Complex Formulations - Lecture 2/3

Explore Quantum Chern-Simons Theory, covering WRT invariants, Resurgence conjecture, and Teichmüller TQFT, with detailed examples and discussions.

• YouTube
• 1 hour 14 minutes
• On-Demand
• Free Video

Institut des Hautes Etudes Scientifiques (IHES)

Resurgence, Quantum Modularity and Quantum Invariants in Three-Manifolds

Explore resurgence in quantum Chern-Simons theory, connecting WRT quantum invariants to BPS q-series. Uncover complex Chern-Simons invariants and prove quantum modularity for Seifert fibered homology spheres.

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

NCCR SwissMAP

Bordered-Sutured Floer Homology as a Sutured TQFT

Explore advanced quantum topology concepts through bordered-sutured Floer homology and its applications as a sutured TQFT in this in-depth lecture by J. Rasmussen.

• YouTube
• 1 hour 6 minutes
• On-Demand
• Free Video

NCCR SwissMAP

Heisenberg Homologies of Configurations in Ribbon Graphs

Explore Heisenberg homologies in ribbon graffs configurations, focusing on quantum topology and representation theory.

• YouTube
• 1 hour 8 minutes
• On-Demand
• Free Video

NCCR SwissMAP

Non-semisimple Link and Manifold Invariants

Explore non-semisimple link and manifold invariants in quantum topology, focusing on representation theory with A. Gainutdinov from CNRS, Université de Tours.

• YouTube
• 1 hour 6 minutes
• On-Demand
• Free Video

NCCR SwissMAP

Derived Skein Modules via Factorization Homology

Explore derived skein modules through factorization homology, delving into categorical symmetries in quantum field theory.

• YouTube
• 1 hour 15 minutes
• On-Demand
• Free Video