Topology Courses and Certifications

IMSA

Low Dimensional Topology and Circle-valued Morse Functions

Explore forbidden minor multibranched surfaces and critical complexes in 3-sphere embeddings. Analyze K5 × S1 and K3,3 × S1 families, critical complexes, and their properties in low-dimensional topology.

• YouTube
• 59 minutes
• Self-Paced
• Conference Talk

IMSA

Low Dimensional Topology and Circle-valued Morse Functions

Explores non almost-fibered knots in 3-sphere, analyzing circular thin positions and Seifert surfaces. Focuses on hyperbolic genus one knots with multiple disjoint Seifert surfaces, demonstrating their complex circular thin positions.

• YouTube
• 51 minutes
• Self-Paced
• Conference Talk

IMSA

Low Dimensional Topology and Circle-valued Morse Functions

Explore instanton Floer homology's surgery formula, its applications in computing 3-manifold invariants, and connections to SU(2)-representations of fundamental groups.

• YouTube
• 58 minutes
• Self-Paced
• Conference Talk

IMSA

Low Dimensional Topology and Circle-valued Morse Functions

Explore singular fibrations in knot exteriors and their extensions over handlebodies, connecting handle-ribbon knots to circular Morse functions in low-dimensional topology.

• YouTube
• 1 hour 2 minutes
• Self-Paced
• Conference Talk

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
• Self-Paced
• Free Video

IMSA

Low Dimensional Topology and Circle-valued Morse Functions

Explore Khovanov homology of torus braids, characterizing simplified complexes and their applications in quantum topology. Gain insights into recent advancements and conjectures in low-dimensional topology.

• YouTube
• 1 hour 1 minute
• Self-Paced
• Conference Talk

IMSA

Low Dimensional Topology and Circle-Valued Morse Functions

Explore the Kakimizu complex for genus one hyperbolic knots, examining its structure, dimensions, and examples across various dimensions in 3-sphere topology.

• YouTube
• 54 minutes
• Self-Paced
• Conference Talk

IMSA

An Application of Symplectic Topology to Algebraic Geometry

Explore symplectic topology's application to algebraic geometry, connecting Rouquier's triangulated category dimension to Krull dimension via homological mirror symmetry.

• YouTube
• 42 minutes
• Self-Paced
• Free Video

Hausdorff Center for Mathematics

Topology of Complexes Arising in Models for Distributed Computing

Explore simplicial models in distributed computing, focusing on chromatic subdivisions and their applications to problems like Weak Symmetry Breaking, leading to new mathematical questions.

• YouTube
• 43 minutes
• Self-Paced
• Free Video

Applied Algebraic Topology Network

Persistence in Functional Topology

Explore functional topology's evolution, connecting persistent homology to critical point theory and calculus of variations. Gain insights into Morse's theory and its application to minimal surfaces.

• YouTube
• 1 hour 5 minutes
• Self-Paced
• Free Video

Kavli Institute for Theoretical Physics

Magnetism and Bands Topology in Nd2Ir2O7 Probed by Raman Scattering Spectroscopy - Natalia Drichko

Explore magnetism and band topology in Nd2Ir2O7 through Raman scattering spectroscopy. Gain insights into quantum aspects of magnetism and complex magnetic materials with entangled spin, orbital, and lattice degrees of freedom.

• YouTube
• 45 minutes
• Self-Paced
• Free Video

Kavli Institute for Theoretical Physics

Magnetism, Topology and the Fractional Quantum Anomalous Hall Effect - Liang Fu

Explore quantum magnetism's frontiers: topology, fractional quantum anomalous Hall effect, and emergent phenomena in complex magnetic materials. Gain insights from cutting-edge research and expert discussions.

• YouTube
• 47 minutes
• Self-Paced
• Free Video

ICTP Mathematics

Lattices in Low-Dimensional Topology

Explore advanced concepts in low-dimensional topology, focusing on lattice structures and their applications in geometric and topological analysis.

• YouTube
• 1 hour 4 minutes
• Self-Paced
• Free Video

ICTP Mathematics

Lattices in Low-Dimensional Topology

Explore advanced concepts in low-dimensional topology, focusing on lattice structures and their applications in geometric and topological analysis.

• YouTube
• 1 hour 6 minutes
• Self-Paced
• Free Video

ICTP Mathematics

Lattices in Low-Dimensional Topology

Explore the fascinating intersection of lattice theory and low-dimensional topology, delving into fundamental concepts and their applications in geometric and topological structures.

• YouTube
• 1 hour 32 minutes
• Self-Paced
• Free Video