Explore the stabilization of unstable outputs in persistent homology computations through this 44-minute lecture by Peter Bubenik. Delve into a general framework for providing stable versions of calculations, with a focus on generating cycles of persistence diagram points. Learn about applied filters, persistent homology, and statistical perspectives in continuous settings. Examine toy examples, noise handling, and preprocessing techniques. Gain insights from this joint work with Paul Bendich and Alexander Wagner, presented as part of the Hausdorff Trimester Program on Applied and Computational Algebraic Topology.