Applied Algebraic Topology Network Courses

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

Modeling and Replicating Persistence Diagrams

Explore modeling and replicating persistence diagrams for statistical inference in topological data analysis. Learn about RST approach, parametric modeling, and improvements for clustered data.

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

Erica Flapan - Topological and Geometric Symmetries of Molecular Structures

Explore topological and geometric approaches to studying symmetries of complex molecular structures, aiding chemists in verifying synthesized molecules' forms through experimental data interpretation.

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

Bernd Sturmfels - Learning Algebraic Varieties from Samples

Explore algebraic varieties through sampling, focusing on topology and geometry. Learn algorithms for determining dimensions and polynomials, with practical applications in Julia.

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

Rachel Levanger - A Comparison Framework for Interleaved Persistence Modules

Explore rigorous tracking of noise in persistent homology, comparing approximation techniques and addressing non-uniform sub-level set filtrations in topological data analysis.

• YouTube
• 1 hour 5 minutes
• On-Demand
• Free Video

An Approximate Nerve Theorem

Explore the Nerve Theorem's application in topological data analysis, focusing on epsilon-acyclic covers and their impact on persistent homology approximations in space filtrations.

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