This course aims to teach students about the central role and historical development of persistent homology in functional topology. The learning outcomes include understanding recent developments in persistence theory, connecting them with classical results in critical point theory and the calculus of variations. Students will learn about the modern view on persistence, providing a new perspective on Morse's theory of functional topology. The course covers topics such as Morse functions, persistence modules, persistence diagrams, and sublevel set persistence. The teaching method involves illustrating concepts through examples and presenting recent joint work. This course is intended for individuals interested in advanced topics in algebraic topology and persistence theory.
Overview
Syllabus
Introduction
Example
Summary
Stability Theorem
Morse Functions
Persistence
Functional topology
Minimal surfaces
Persistence approach
Persistence modules
Persistence diagram
Butane persistent homology
Sublevel set persistence
Check vs Singular
Dry Considerations
Taught by
Applied Algebraic Topology Network
