3-Manifolds Courses and Certifications

International Mathematical Union

Jacob Rasmussen - Floer Homology of 3-Manifolds with Torus Boundary

Explore advanced concepts in Floer homology, focusing on 3-manifolds with torus boundary. Gain insights into cutting-edge mathematical research and its applications in topology.

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

QuantumTopology

Stable Maps and Branched Shadows of 3-Manifolds

Explore stable maps and branched shadows in 3-manifolds, delving into advanced concepts in quantum topology and geometric structures.

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

IMSA

Bounds on Morse-Novikov Numbers of 3-Manifolds

Explore bounds on Morse-Novikov numbers of 3-manifolds, examining circle-valued Morse functions and their critical points, with applications to knot theory and topology.

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

ICTP Mathematics

Slope Detection in 3-Manifolds

Explore key concepts in 3-manifold topology, including slope detection, Lagrangian theory, and foliations. Learn about conjectures, theorems, and algorithms in this advanced mathematical field.

• YouTube
• 1 hour 2 minutes
• On-Demand
• Free Video

Simons Semester on Dynamics

Classifying Pseudo-Anosov Flows on 3-Manifolds - Lecture 1

Explore the intricacies of classifying pseudo-Anosov flows on 3-manifolds in this engaging lecture by Kathryn Mann from Cornell University. Delve into the collaborative work with Barthelmé, Fenley, and Frankel as they tackle this complex topic. Discover…

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

IMSA

From Turaev to Rokhlin via VOA Characters and Curve Counting

Explore q-series invariants of 3-manifolds, their properties, and connections to topology, vertex algebras, and enumerative problems. Gain insights into recent developments in this mathematical field.

• YouTube
• 1 hour 12 minutes
• On-Demand
• Free Video

IMSA

From Turaev to Rokhlin via VOA Characters and Curve Counting

Explore q-series invariants of 3-manifolds, their properties, and connections to topology, vertex algebras, and enumerative problems. Gain insights into Spin-C structures and related mathematical concepts.

• YouTube
• 1 hour 5 minutes
• On-Demand
• Free Video

IMSA

Cohomological Donaldson-Thomas Invariants of 3-Manifolds

Explore Morse homology of complex Chern-Simons functional, its connections to 4D supersymmetric gauge theories, skein modules, and Donaldson-Thomas invariants in 3-manifolds.

• YouTube
• 1 hour 6 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

Ph. Korablev - Skein-Invariants of 3-Manifolds

Explore skein-invariants of 3-manifolds in this advanced topology lecture, delving into complex mathematical concepts and their applications in quantum topology.

• YouTube
• 1 hour 27 minutes
• On-Demand
• Free Video

QuantumTopology

Calculation of Casson Invariant for 3-Manifolds

Explore the calculation methods for Casson invariant in 3-manifolds, a crucial topological invariant in low-dimensional topology and knot theory.

• YouTube
• 1 hour 31 minutes
• On-Demand
• Free Video

QuantumTopology

On Matveev’s Complexity of Classical and Virtual 3 Manifolds

Explore Matveev's complexity theory for classical and virtual 3-manifolds, delving into advanced topological concepts and their applications in quantum topology.

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

IMSA

Cohomological Donaldson-Thomas Invariants of 3-Manifolds - Part 2

Explore Morse homology of complex Chern-Simons functional, its connections to supersymmetric gauge theories, skein modules, and Donaldson-Thomas invariants in 3-manifolds.

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

Banach Center

Categorification of Quantum Invariants: From Knots to 3-Manifolds - Part 1

Explore categorification of quantum invariants, focusing on knots and 3-manifolds. Delve into advanced mathematical concepts with expert Sergei Gukov from Caltech and Dublin IAS.

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

BIMSA

Curvature-Homogeneous Riemannian 3-Manifolds and Integrable Systems

Explore curvature-homogeneous Riemannian 3-manifolds, surveying known examples and recent discoveries. Delve into connections with integrable systems, particularly Toda lattices, to construct new explicit examples.

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