Persistence in Functional Topology
Explore the historical development and central role of persistent homology in functional topology through this insightful lecture. Delve into recent developments in persistence theory and their connections to classical results in critical point theory and calculus of variations. Discover how the modern perspective on persistence offers a fresh and clarifying view of Morse's theory of functional topology, which played a crucial role in the first proof of unstable minimal surfaces by Morse and Tompkins. Examine topics such as stability theorems, Morse functions, persistence modules, persistence diagrams, and sublevel set persistence. Gain a deeper understanding of the application of persistent homology beyond applied topology, including its relevance to butane persistent homology and the comparison between Check and Singular approaches.