Vietoris-Rips Persistent Homology, Injective Metric Spaces, and The Filling Radius
Offered By: Applied Algebraic Topology Network via YouTube
Course Description
Overview
Explore the connections between Vietoris-Rips persistent homology, injective metric spaces, and the filling radius in this comprehensive lecture. Delve into a geometric approach for generating persistent homology of metric spaces by embedding them into larger ambient metric spaces. Discover how this method relates to the standard Vietoris-Rips simplicial filtration, and learn about the isomorphism between these approaches when the ambient space is injective. Examine applications of this isomorphism, including characterizing intervals in persistence barcodes, analyzing products and metric gluings of metric spaces, and establishing bounds on barcode interval lengths. Investigate the relationship between geometric persistent homology and Gromov's filling radius concept, exploring implications for the homotopy type of Vietoris-Rips complexes of spheres and rigidity results for spheres based on their Vietoris-Rips persistence barcodes.
Syllabus
Facundo Mémoli: Vietoris-Rips Persistent Homology, Injective Metric Spaces, and The Filling Radius
Taught by
Applied Algebraic Topology Network
Related Courses
Topology for Time SeriesData Science Dojo via YouTube Studying Fluid Flows with Persistent Homology - Rachel Levanger
Institute for Advanced Study via YouTube Persistence Diagram Bundles- A Multidimensional Generalization of Vineyards
Applied Algebraic Topology Network via YouTube GPU Accelerated Computation of VR Barcodes in Evaluating Deep Learning Models
Applied Algebraic Topology Network via YouTube New Results in Computing Zigzag and Multiparameter Persistence
Applied Algebraic Topology Network via YouTube