BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Henry Adams (Colorado State University) DTSTART:20220314T103000Z DTEND:20220314T113000Z DTSTAMP:20260422T135430Z UID:BilTop/39 DESCRIPTION:Title: An introduction to Vietoris-Rips complexes\nby Henry Adams (Colorado S tate University) as part of Bilkent Topology Seminar\n\nLecture held in SB -Z11.\n\nAbstract\nI will give an introduction to Vietoris-Rips complexes and their uses in applied and computational topology. If a dataset is samp led from some unknown underlying space (say a manifold)\, then as more and more samples are drawn\, the Vietoris-Rips persistent homology of the dat aset converges to the Vietoris-Rips persistent homology of the manifold. B ut little is known about Vietoris-Rips complexes of manifolds. An exceptio n is the case of the circle: I will describe how as the scale parameter in creases\, the Vietoris-Rips complexes of the circle obtain the homotopy ty pes of the circle\, the 3-sphere\, the 5-sphere\, ...\, until finally they are contractible. Much less is known about Vietoris-Rips complexes of sph eres. I will also briefly explain how Vietoris-Rips complexes relate to ge neralizations of the Borsuk-Ulam theorem and to Gromov-Hausdorff distances between spheres.\n LOCATION:https://researchseminars.org/talk/BilTop/39/ END:VEVENT END:VCALENDAR