Applied Algebraic Topology Network Courses

Oliver Vipond - Local Equivalence of Metrics for Multiparameter Persistence Modules

Explore local equivalence of metrics for multiparameter persistence modules, focusing on fibered bar codes' discriminative power and stability in topological data analysis.

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

Topology in Chemistry Applications

Explore topological data analysis in chemistry, focusing on molecular relationships, graph theory, and network analysis to extract new insights from chemical data.

• YouTube
• 1 hour 7 minutes
• On-Demand
• Free Video

Catastrophe Theory

Explore catastrophe theory, covering critical points, germs, classification theorems, unfoldings, and elementary catastrophes. Visualize concepts and discover applications in chemistry.

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

TDALabs - Some of TDA's Greatest Hits in Interactive Python

Interactive exploration of TDA's key applications using Python, covering time series analysis, image processing, 3D shape clustering, and more. Hands-on examples showcase TDA's versatility and practical uses.

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

Henry Adams and Enrique Alvarado - An Introduction to Morse Theory

Explore Morse theory's applications in topology, including CW complexes, key theorems, and simplification techniques, with real-world examples in material science.

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

Cyber Infrastructure for Science Gateways

Explore state-of-the-art computational resources for molecular sciences through science gateways. Learn about gateway architectures, workflow deployment, and integration of visualization and post-processing tools.

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

An Introduction to Mapper

Explore Mapper, a topological data analysis technique for visualizing complex datasets. Learn its principles, applications, and how it reveals hidden structures through clustering and graph representation.

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

Liz Munch - Featurization of Persistence Diagrams Using Template Functions for ML Tasks

Explore topological data analysis and persistence diagrams for machine learning, focusing on featurization techniques using template functions to map complex data into Euclidean space.

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

Homological Percolation: The Formation of Giant Cycles

Explore homological percolation, analyzing giant cycles in random structures and their phase transitions. Learn to differentiate signal from noise in persistence diagrams and discover connections to Euler characteristic curves.

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

Why Should Q=P in the Wasserstein Distance Between Persistence Diagrams?

Explore Wasserstein distance in persistence diagrams, focusing on q=p choice. Covers geometric implications, stability results, algebraic versions, and computational advantages for central tendencies.

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

Parameterized Complexity of Quantum Invariants of Knots

Explore quantum invariants of knots, their parameterized complexity, and efficient algorithms for computation using graphical calculus and tree embeddings.

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

Geometric Interpretation of Persistence

Explore geometric interpretations of persistence in algebraic topology, covering space reconstruction, one-dimensional persistent homology classification, and detection of contractible geodesics using higher-dimensional features.

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

The Magnitude of a Metric Space

Explore the magnitude of metric spaces, an isometric invariant encoding volume, dimension, and capacity. Learn about current research and its connection to persistent homology.

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

Limit Theorems in Topological Data Analysis

Explore limit theorems in topological data analysis, focusing on barcodes, persistence modules, and random persistence modules. Learn about convergence proofs and expectations for uniform distributions on compact submanifolds.

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

Ulrich Bauer - Persistence Diagrams as Diagrams

Explore persistence diagrams as categorical functors, examining their structure, stability, and relationships to matchings. Learn about new constructions and theorems in this advanced algebraic topology lecture.

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