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The Gromov-Hausdorff Distance Between Spheres

Offered By: Applied Algebraic Topology Network via YouTube

Tags

Riemannian Geometry Courses Topology Courses Algebraic Topology Courses Topological Data Analysis Courses

Course Description

Overview

Explore a comprehensive lecture on the Gromov-Hausdorff distance between spheres, delivered by Facundo Mémoli. Delve into this fundamental tool in Riemannian geometry, applied geometry, and topology. Learn about the challenges in determining precise values of the distance between metric spaces and discover recent results that enable calculating the exact Gromov-Hausdorff distance between specific pairs of spheres with geodesic distance. Gain insights into key concepts such as correspondences, distortion of relations, simple bounds, surjections, lower bounds, persistence, and filling radius. Examine the intricacies of reverse Gromov-Hausdorff and antibodies preservation. This 58-minute talk, part of the "Topological Data Analysis - Theory and Applications" workshop, offers a deep dive into advanced mathematical concepts for those interested in geometric and topological analysis.

Syllabus

Intro
Background
Notation
Correspondences
Distortion of a relation
Simple bounds
Surjections
Lower Bounds
Persistence
Filling Radius
The correspondence
The lower bound
Summary
Reverse GromovHausdorff
Antibodies Preservation
Comments


Taught by

Applied Algebraic Topology Network

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