Discrete Morse Theory Courses and Certifications

Applied Algebraic Topology Network

Graph Reconstruction via Discrete Morse Theory

Explore graph reconstruction using discrete Morse theory, focusing on geometric graphs and density data. Learn about theoretical guarantees and applications in road network reconstruction.

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

Applied Algebraic Topology Network

Hardness Results in Discrete Morse Theory for 2-Complexes

Explore inapproximability and parameterized complexity in discrete Morse theory for 2-complexes, focusing on minimizing critical simplices and presenting new hardness results and an approximation algorithm.

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

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

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

Applied Algebraic Topology Network

Topological Uncertainty and Representations for Biomedical Image Analysis

Innovative approach to biomedical image analysis using topological structures and uncertainty, enhancing segmentation accuracy and enabling interactive annotation for fine-scale delineation.

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

Applied Algebraic Topology Network

Morse Theory for Group Presentations and the Persistent Fundamental Group

Discrete Morse theory refinement for CW-complexes, with applications in combinatorial group theory and topological data analysis, including persistent fundamental group computation.

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

Applied Algebraic Topology Network

On the Inverse Problem Between Discrete Morse Functions and Merge Trees

Explore the inverse relationship between discrete Morse functions on graphs and merge trees, uncovering how to find all functions that produce a given merge tree structure.

• YouTube
• 46 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

Topological Complexity Seminar - Applied Algebraic Topology Network

Explore advanced mathematical concepts in topological complexity through expert seminars covering motion planning, manifold theory, and algebraic topology applications.

• YouTube
• 1 day 17 hours 29 minutes
• On-Demand
• Free Video

Applied Algebraic Topology Network

Beyond TDA - Persistent Functions and Applications in Data Sciences 2021

Explore advanced topological data analysis methods beyond traditional TDA, including persistent functions, spectral complexes, and sheaf theory for machine learning applications.

• YouTube
• 18 hours 2 minutes
• On-Demand
• Free Video

Applied Algebraic Topology Network

Applied Algebraic Topology Tutorial Collection - Spring 2021

Dive into topological data analysis through 38 specialized tutorials covering persistent homology, complexes, algorithms, and real-world applications in this comprehensive workshop series.

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

Hausdorff Center for Mathematics

Ulrich Bauer: Ripser - Efficient Computation of Vietoris–Rips Persistence Barcodes

Explore efficient computation of Vietoris-Rips persistence barcodes using Ripser software. Learn about matrix reduction algorithms, persistent cohomology, and discrete Morse theory applications in topological data analysis.

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

Applied Algebraic Topology Network

Bridging Applied and Quantitative Topology 2022

Explore advanced connections between applied and quantitative topology through expert lectures on persistent homology, deep learning applications, and geometric data analysis.

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