Applied Algebraic Topology Network Courses

Harish Chintakunta - Topological Data Analysis and Signal Processing

Explore topological data analysis in signal processing, covering embedding techniques, harmonic effects, and applications in seizure prediction and power grid oscillation detection.

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

John Harer - Topological Data Analysis and Machine Learning

Explore topological data analysis and machine learning, covering methodology, examples, dimension reduction, and advanced techniques for feature extraction and classification.

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

Michael Lesnick - Algebraic Stability of Zigzag Persistence Modules

Explore algebraic stability in zigzag persistence modules, covering key concepts, theorems, and applications in topological data analysis and computational topology.

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

Sheaf Based Modeling of Wireless Communications

Explore sheaf-based modeling for wireless communications, covering topology, simplicial complexes, interference, and network activation. Learn about persistence, homological invariants, and simulation examples.

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

Larry Wasserman - Robust Topological Inference

Explore robust topological inference with Larry Wasserman, covering persistence, confidence bands, bootstrap methods, and optimal tuning for data analysis and statistical modeling.

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

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