Explore the application of persistent homology in topological data analysis through this comprehensive lecture on computable stability for persistence rank function machine learning. Delve into the challenges of using persistent homology barcodes and diagrams in statistical settings, and discover how persistent rank functions and rank invariants offer alternative representations that are more easily integrated into machine learning and inferential tasks. Examine the functional nature of these invariants and their compatibility with Functional Data Analysis. Learn about three practical applications of rank functions and biparameter rank invariants to real and simulated data. Investigate stability results for rank functions and rank invariants under L^p metrics, crucial for the discussed applications. Gain insights from the collaborative work of Inés García-Redondo, Qiquan Wang, Pierre Faugère, Anthea Monod, and Gregory Henselman-Petrusek in this 57-minute lecture presented by the Applied Algebraic Topology Network. Read more