Don Sheehy - Persistent Homology of Lipschitz Extensions
Explore the theory of persistent homology in Lipschitz extensions through this insightful lecture by Don Sheehy. Delve into the analysis of metric spaces and real-valued Lipschitz functions, examining how to derive information about persistent homology from sublevel set filtrations. Investigate the challenges of working with sample data without guarantees of density or quality. Learn about the innovative concept of sub-barcodes as an alternative to bottleneck distance for theoretical barcode guarantees. Discover techniques for computing barcodes from Lipschitz extensions that serve as sub-barcodes for all Lipschitz functions agreeing with given sample points. Gain valuable insights into advanced topics in applied algebraic topology and their applications in data analysis.