Morse Theory Courses and Certifications

Applied Algebraic Topology Network

Claudia Landi - Multi-parameter Persistence from the Viewpoint of Discrete Morse Theory

Explore multi-parameter persistence through discrete Morse theory, connecting combinatorial properties of critical cells to algebraic properties of persistence modules in topological data analysis.

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

Applied Algebraic Topology Network

Discrete Morse Theory Meets Multi-Parameter Persistence

Exploring connections between discrete Morse theory and multiparameter persistence in topological data analysis, focusing on critical cells, fibered rank invariant, and computational efficiency.

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

Applied Algebraic Topology Network

An Application of Discrete Morse Theory to Robot Motion Planning

Explore discrete Morse theory and its variants, learning how to apply this mathematical concept to develop continuous motion planning algorithms for autonomous devices.

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

IMSA

Stability Structures in Holomorphic Morse-Novikov Theory

Explore complex symplectic manifolds, Floer theory, and Morse-Novikov theory. Delve into analytic questions of convergence and generalization to almost-complex cases in this advanced mathematical lecture.

• YouTube
• 1 hour 6 minutes
• On-Demand
• Free Video

Applied Algebraic Topology Network

Bridging Persistent Homology and Discrete Morse Theory with Applications to Shape Reconstruction

Explore the connection between persistent homology and discrete Morse theory, unifying key concepts and applying insights to shape reconstruction in computational topology.

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

Applied Algebraic Topology Network

Discrete Morse Theory - Introduction and Research Directions

Explore discrete Morse theory's fundamentals and cutting-edge research on gradient vector fields, merge trees with cycles, and open simplicial complexes applications.

• YouTube
• 1 hour 9 minutes
• On-Demand
• Free Video

Mathemaniac

The More General Euler Characteristic Formula - Understanding Surface Topology

Explore the deeper implications of Euler's characteristic formula as an inequality, examining its relationship with genus, Morse functions, and topological surfaces through intuitive explanations.

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

Applied Algebraic Topology Network

Applied Algebraic Topology Methods, Computation, and Science - ATMCS/AATRN 2020

Explore cutting-edge research in applied algebraic topology through expert presentations on persistence diagrams, homology, and computational methods for data analysis.

• YouTube
• 17 hours 43 minutes
• On-Demand
• Free Video

Applied Algebraic Topology Network

DELTA - Descriptors of Energy Landscape by Topological Analysis Webinar 2020

Explore topological data analysis methods for characterizing energy landscapes in chemical transformations and molecular systems.

• YouTube
• 8 hours 21 minutes
• On-Demand
• Free Video

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 Video

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 Video

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 Video

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 Video

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
• On-Demand
• Conference Talk

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 Video