Morse Theory Courses and Certifications

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
• On-Demand
• Conference Talk

A New Model for Stable Homotopy - Extending Pontryagin-Thom Construction

Explore a new model for stable homotopy, extending the Pontryagin-Thom construction to the entire stable homotopy category through the lens of bordism theory.

• YouTube
• 1 hour 3 minutes
• On-Demand
• Free Online Course

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
• On-Demand
• Free Online Course

Applied Algebraic Topology Network

Henry Adams and Enrique Alvarado - An Introduction to Morse Theory

Explore Morse theory's applications in topology, including CW complexes, key theorems, and simplification techniques, with real-world examples in material science.

• YouTube
• 40 minutes
• On-Demand
• Free Online Course

Applied Algebraic Topology Network

Vidit Nanda - Morse Theory for Local Coefficients

Explore Morse theory with local coefficients, covering cohomogeneous complexes, wave graphs, and isomorphisms. Delve into advanced topics and theorems in algebraic topology.

• YouTube
• 57 minutes
• On-Demand
• Free Online Course

Applied Algebraic Topology Network

An Upper Bound on the Topological Complexity of Discriminantal Varieties

Explore upper bounds on topological complexity of discriminantal varieties, with applications to configuration spaces. Combines Morse theory, equivariant homotopy theory, and complex geometry.

• YouTube
• 54 minutes
• On-Demand
• Free Online Course

Applied Algebraic Topology Network

Moduli Spaces of Morse Functions for Persistence

Exploring Morse functions on surfaces, focusing on decomposition, elementary moves, and embeddings. Insights into persistence barcodes and the inverse problem through nesting posets of level sets.

• YouTube
• 55 minutes
• On-Demand
• Free Online Course

Applied Algebraic Topology Network

Generalized Morse Theory of Distance Functions to Surfaces for Persistent Homology

Unifying distance fields, persistent homology, and Morse theory to quantify complex shape textures, with applications in characterizing vascular structures in leukemia samples.

• YouTube
• 44 minutes
• On-Demand
• Free Online Course

Applied Algebraic Topology Network

Computation of Reeb Graphs in a Semi-Algebraic Setting

Explore semi-algebraic geometry in applied topology, focusing on Reeb graphs and spaces. Learn about an efficient algorithm for computing semi-algebraic descriptions of Reeb graphs.

• YouTube
• 31 minutes
• On-Demand
• Free Online Course

International Mathematical Union

Mean Curvature and Variational Theory

Explores recent developments in prescribing mean curvature equations, focusing on existence theory, min-max theory for CMC/PMC surfaces, and Morse theory for area functional. Includes solution to Multiplicity One Conjecture.

• YouTube
• 45 minutes
• On-Demand
• Free Online Course

Applied Algebraic Topology Network

Barcodes for the Topological Analysis of Gradient-Like Vector Fields

Explore topological analysis of gradient-like vector fields using barcodes. Learn about chain complexes, parametrization, and applications in smooth and discrete settings, with insights on stability and approximation.

• YouTube
• 1 hour 6 minutes
• On-Demand
• Free Online Course

Galileo Galilei Institute

On the Fukaya-Morse A-infinity Category

Explore the intricacies of Fukaya-Morse A-infinity category with Pavel Mnev, delving into advanced mathematical concepts and their applications in topology and geometry.

• YouTube
• 1 hour 15 minutes
• On-Demand
• Free Online Course