BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Katharine Turner (Australian National University) DTSTART:20200807T050000Z DTEND:20200807T060000Z DTSTAMP:20260423T021505Z UID:APATG/2 DESCRIPTION:Title: Wa sserstein Stability for Persistence Diagrams\nby Katharine Turner (Aus tralian National University) as part of Asia Pacific Seminar on Applied To pology and Geometry\n\n\nAbstract\nThe stability of persistence diagrams i s among the most important results in applied and computational topology. Most results in the literature phrase stability in terms of the bottleneck distance between diagrams and the infinity-norm of perturbations. This ha s two main implications: it makes the space of persistence diagrams rather pathological and it is often provides very pessimistic bounds with respec t to outliers. In this talk I will discuss new stability results with resp ect to the p-Wasserstein distance between persistence diagrams. I will giv e an elementary proof for the setting of functions on sufficiently finite spaces in terms of the p-norm of the perturbations. I will also apply the results to a wide range of applications in topological data analysis (TDA) including topological summaries\, persistence transforms and the special but important case of Vietoris-Rips complexes. This is joint work with Pri moz Skraba (see https://arxiv.org/abs/2006.16824). \n\nThe assumed knowled ge for the talk: \n\n The persistent homology and persistence diagram f or the sub-level set filtration of a real-valued function on a finite simp licial complex.\n\n The Vietoris-Rips complex of a set of points in Eu clidean space.\n LOCATION:https://researchseminars.org/talk/APATG/2/ END:VEVENT END:VCALENDAR