Topology Courses and Certifications

QuantumTopology

Topology of Large Random Spaces

Explore the fascinating realm of large random spaces and their topological properties in this insightful lecture by mathematician Michael Farber.

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

QuantumTopology

Knotoids as Cobordisms

Explore knotoids as cobordisms in this advanced topology lecture, delving into mathematical concepts and their applications in quantum theory and knot theory.

• YouTube
• 1 hour 25 minutes
• On-Demand
• Free Video

QuantumTopology

Penner Coordinates for Closed Surfaces

Explore Penner coordinates for closed surfaces, delving into mathematical concepts and applications in quantum topology.

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

QuantumTopology

A Census of Tetrahedral Hyperbolic Manifolds

Explore tetrahedral hyperbolic manifolds in this comprehensive census, examining their properties, classifications, and implications for quantum topology research.

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

QuantumTopology

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

QuantumTopology

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

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

IMSA

On Mapping Class Groups of Non-Orientable Surfaces

Exploración de la estructura y cohomología de grupos de clases de mapeo en superficies no orientables, incluyendo resultados recientes sobre el plano proyectivo y la botella de Klein.

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

Alan Turing Institute

The Shape of Data

Exploring how topology can extract new insights from abundant data, focusing on innovative applications of abstract mathematics to deepen our understanding of complex datasets.

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

FlippedNormals

Is Good Topology Overrated?

Exploring the necessity of good topology in 3D modeling, discussing when to use Zremesh, proper topology, or decimation, and examining the impact on design time, deformation, and overall efficiency.

• YouTube
• 23 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

IMSA

Isotropic Killing Vector Fields and Related Structures on Complex Surfaces

Exploration of isotropic Killing vector fields on complex surfaces, examining integrable structures, topology, and geometric properties in 4-dimensional manifolds with split-signature metrics.

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

IMSA

Generalized Logarithmic Transformation in Exotic Spheres and Homotopy Hopf Manifolds

Explore generalized logarithmic transformations in topology, including $\star$-diagrams, spherical T-duality, and applications to exotic spheres and homotopy Hopf manifolds.

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

IMSA

Spherical T-Duality Meets Exotic Spheres and Homotopy Hopf Manifolds

Explore spherical T-duality, its relation to 7-dimensional homotopy spheres, and implications for complex structures on exotic manifolds in this advanced mathematical discussion.

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

Applied Algebraic Topology Network

Topology in Digital Sound Synthesis

Exploring topological concepts in digital sound synthesis, from oscillatory algorithms to wave equations and filter theory, with applications in computational audio generation.

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