Quantum Topology Courses and Certifications

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

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

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

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

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

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

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

25.03.2020 Ф.Г. Кораблёв - Автоморфизмы раскрасок и инварианты узлов

Исследование автоморфизмов раскрасок и их связи с инвариантами узлов в топологии. Анализ современных методов и подходов в этой области математики.

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

IMSA

Quantization of Moduli Spaces of Local Systems at Roots of Unity

Explore quantization of G-local system moduli spaces on decorated surfaces, discussing applications to quantum topology and quantum group representations.

• YouTube
• 1 hour 3 minutes
• On-Demand
• Free Video