Applied Algebraic Topology Network Courses

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

Ran Levi - Bedlewo: Topological Analysis of Neural Networks

Explore topological analysis of neural networks using algebraic topology techniques on biologically accurate digital reconstructions, revealing structural and functional insights into brain connectivity.

• YouTube
• 1 hour 10 minutes
• Self-Paced
• Free Video

David Meyer - Some Algebraic Stability Theorems for Generalized Persistence Modules

Algebraic stability theorems for generalized persistence modules, exploring interleaving metrics, bottleneck metrics, and isometry theorems in the context of poset algebras and quiver representations.

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

Constructions of K-Regular Maps Using Finite Local Schemes

Explore k-regular maps and interpolation theory in algebraic geometry. Learn construction methods, bounds, and applications to continuous function interpolation using advanced mathematical concepts.

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

Bedlewo- Topological Complexity and the Motion Planning Problem in Robotics

Explore topological complexity in robotics motion planning, its algebraic topology properties, recent developments, and research trends in this rich field.

• YouTube
• 1 hour 33 minutes
• Self-Paced
• Free Video

Pavle Blagojević - Bedlewo: Shadows of Cohen's Vanishing Theorem

Explore Cohen's Vanishing theorem and its applications in algebraic topology, geometry, and combinatorics. Discover its impact on configuration spaces and measure partition problems.

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

Vanessa Robins - Persistence Diagrams of Bead Packings

Exploring grain-scale mechanisms in granular crystallization using X-ray tomography and persistent homology, revealing key formation processes of tetrahedral and octahedral pores in spherical bead packings.

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

Pawel Dlotko - A Few Simple Stories on Topology in Action

Explore practical applications of computational topology in material science, dynamical systems, and brain research. Learn how theory and algorithms work together to solve real-world problems.

• YouTube
• 1 hour 3 minutes
• Self-Paced
• Free Video

Persistence Images

Explore persistent homology and persistence images for topological data analysis. Learn to convert persistence diagrams into vector representations for machine learning applications.

• YouTube
• 1 hour 2 minutes
• Self-Paced
• Free Video

Estimating the Reach of a Manifold

Explore estimating manifold reach in geometric inference, covering problem formulation, statistical models, and minimax estimates for global and local cases.

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

Anthony Bak - Spaces of Shapes Persistent Homology for Drug Discovery

Explore persistent homology in drug discovery, focusing on structure-based design, chemical compound analysis, and machine learning applications for virtual screening and classification.

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