Applied Algebraic Topology Network Courses

Quantum Topological Data Analysis - Part 1

1 rating

Explore quantum persistent homology algorithms for pattern recognition in data, leveraging quantum computing's potential to enhance traditional Topological Data Analysis methods and improve efficiency.

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

Kelin Xia - Persistent Function Based Machine Learning for Drug Design

1 rating

Exploring persistent function-based machine learning for drug design, focusing on novel molecular representations and their application in improving predictive models for drug discovery.

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

Data Analysis with Merge Trees

Explore merge trees as topological summaries in data analysis, including their advantages over persistence diagrams, computational challenges, and applications in functional data and medical imaging.

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

Coupling Time-Aware Multipersistence with Graph CNNs for Time Series Forecasting

Explore innovative time series forecasting using Graph Neural Networks and multipersistence, applied to traffic flow, cryptocurrency prices, and COVID-19 hospitalizations.

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