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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• Free Video

How Optimal Transport Can Help Us to Determine Curvature of Complex Networks

Explore Ollivier Ricci curvature in complex networks, its applications in network analysis, and implementation in chemical reaction networks using optimal transport theory.

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

Graph Representation Learning and Its Applications to Biomedicine

Graph representation learning techniques for biomedical applications, focusing on SubGNN for disentangled subgraph embeddings and their use in predicting disease treatments and safe drug combinations.

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

Liquid Crystals Dynamics - What Persistent Homology Reveals

Explore liquid crystal phase transitions through persistent homology, revealing thermodynamic features and structural changes in nanocomposites using advanced data analysis techniques.

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

Topological Complexity of Pure Graph Braid Groups

Explore topological complexity in graph braid groups, focusing on Farber's conjecture about ordered configuration spaces and its implications for topological robotics.

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

Nonlinear Dynamics in an Age of Heuristic Science

Explore nonlinear dynamics through combinatorial topology, offering efficient computational methods and new perspectives for multiscale systems and data-driven science in biology and engineering.

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