Applied Algebraic Topology Network Courses

Matthew Kahle - Topology of Configuration Spaces of Hard Spheres

Explore configuration spaces, homology, and topology in hard sphere systems. Learn about critical points, computational approaches, and theoretical foundations in applied algebraic topology.

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

Katharine Turner - PCA of Persistent Homology Rank Functions with Case Studies

Explore persistent homology rank functions through PCA, featuring case studies and insights into topological data analysis techniques.

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

Nonlinear Dynamics, High Dimensional Data, and Persistent Homology

Explore nonlinear dynamics, high-dimensional data analysis, and persistent homology with Konstantin Mischaikow. Learn about algebraic topology applications, persistence diagrams, and recent advancements in data science.

• YouTube
• 1 hour 9 minutes
• Self-Paced
• Free Video

Tamal Dey - A Framework for Topological Summarization

Explore topological summarization frameworks, covering concepts like nerve complexes, multiscale mapper, persistence diagrams, and stability in hierarchical covers. Gain insights into advanced computational topology techniques.

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

Omer Bobrowski - Maximally Persistent Cycles in Random Geometric Complexes

Explore persistent cycles in random geometric complexes, examining key tools, processes, and results. Gain insights into random graph theory and future research directions.

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

Sanjeevi Krishnan - Homological Programming

Explore algebraic topology applications in programming, covering pursuit-evasion problems, positive cones, Alexander duality, and directed topology, with insights into decomposability and computational aspects.

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

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
• Self-Paced
• Free Video

Applied Algebraic Topology Network - Student Seminar Introduction to JavaPlex

Learn to use JavaPlex for topological data analysis, covering key concepts like witness complexes, data representation, and visualization tools. Ideal for students exploring computational topology.

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

Washington Mio - Stable Homology of Metric Measure Spaces

Explore stable homology in metric measure spaces, covering Wasserstein distance, local homology stability, and applications in data analysis and taxonomic classification.

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

Gunnar Carlsson - Local to Global Principles in Persistent Homology

Explore persistent homology's local-to-global principles, computational methods, and applications in topology and data analysis with expert Gunnar Carlsson.

• YouTube
• 1 hour 2 minutes
• Self-Paced
• Free Video

José Samper Seminar - Higher Chordality

Explore higher chordality in algebraic topology, covering community algebra, linear resolution, graphs, polytopes, and complex links. Gain insights into advanced mathematical concepts.

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

Bala Krishnamoorthy: Linear Programming in Geometric Measure Theory

Explore geometric measure theory through linear programming, examining integral currents, simplicial flat norm, and polyhedral approximation. Discover applications in median shape analysis.

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

Benjamin Schweinhart - Statistical Topology of Random Cell Complexes, and Applications

Explore statistical topology of random cell complexes, covering curvature flow, grain growth, graph limits, and computational evidence for steady state hypothesis.

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

Greg Malen - Collapsibility of Random Clique Complexes

Explore k-collapsibility in random clique complexes, examining dimensional faces, strong connectivity, and homology implications for topological data analysis.

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

Category Weight Estimates of Minimal Triangulations

Explore LS-category methods for estimating minimal triangulations of manifolds and polyhedra, focusing on lower bounds for vertex counts in space triangulations.

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