BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Qingsong Wang (The Ohio State University) DTSTART:20211005T200000Z DTEND:20211005T210000Z DTSTAMP:20260423T004134Z UID:TDGA/3 DESCRIPTION:Title: The Persistent Topology of Optimal Transport Based Metric Thickenings\nby Qingsong Wang (The Ohio State University) as part of Topology\, Geometry\ , & Data Analysis (TGDA) Seminar\n\n\nAbstract\nA metric thickening of a g iven metric space X is any metric space admitting an isometric embedding o f X. Thickenings have found use in applications of topology to data analys is\, where one may approximate the shape of a dataset via the persistent h omology of an increasing sequence of spaces. We introduce two new families of metric thickenings\, the p-Vietoris–Rips and p-Čech metric thicken ings for any p between 1 and infinity\, which include all measures on X wh ose p-diameter or p-radius is bounded from above\, equipped with an optima l transport metric. These families recover the previously studied Vietoris –Rips and Čech metric thickenings when p is infinity. As our main contr ibution\, we prove a stability theorem for the persistent homology of p-Vi etoris–Rips and p-Čech metric thickenings\, which is novel even in the case p is infinity. In the specific case p equals 2\, we prove a Hausmann- type theorem for thickenings of manifolds\, and we derive the complete lis t of homotopy types of the 2-Vietoris–Rips thickenings of the sphere as the scale increases. This is joint work with Henry Adams\, Facundo Mémoli and Michael Moy.\n LOCATION:https://researchseminars.org/talk/TDGA/3/ END:VEVENT END:VCALENDAR