Persistent Homotopy Groups of Metric Spaces
Offered By: Applied Algebraic Topology Network via YouTube
Course Description
Overview
Explore persistent homotopy groups of metric spaces in this 46-minute lecture from the Applied Algebraic Topology Network. Delve into the study of persistent homotopy groups of compact metric spaces and their stability properties in the Gromov-Hausdorff sense. Discover how the classical fundamental group exhibits a tree-like structure and an associated ultrametric under mild assumptions. Examine pairs of filtrations that are confounded by persistent homology but distinguished by persistent homotopy groups. Learn about persistent rational homotopy groups and their advantages in providing additional information compared to persistent homology. Cover topics including motivation, previous work, discrete homotopic theory, persistent fundamental groups, stability, dendrograms, computational perspectives, and interleaving distance.
Syllabus
Introduction
Motivation
Previous work
Discrete homotopic theory
Review
Persistent fundamental group
Stability
Example
Dendrograms
Computational perspective
Interleaving distance
Questions
Taught by
Applied Algebraic Topology Network
Related Courses
Social Network AnalysisUniversity of Michigan via Coursera Intro to Algorithms
Udacity Data Analysis
Johns Hopkins University via Coursera Computing for Data Analysis
Johns Hopkins University via Coursera Health in Numbers: Quantitative Methods in Clinical & Public Health Research
Harvard University via edX