BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:David Lenze (Karlsruhe Institute of Technology) DTSTART:20260128T160000Z DTEND:20260128T170000Z DTSTAMP:20260423T021350Z UID:VSGS/124 DESCRIPTION:Title: R igidity of the Ebin metric\nby David Lenze (Karlsruhe Institute of Tec hnology) as part of Virtual seminar on geometry with symmetries\n\n\nAbstr act\nIn 1970\, Ebin introduced a natural L2-type metric on the infinite-di mensional space of Riemannian metrics over a given manifold. Though the in finite dimensional geometry of this space has been extensively-studied\, a new metric perspective emerged in 2013 when Clarke showed that the comple tion with respect to the Ebin metric turns out to be a CAT(0) space.\n\nRe cently\, Cavallucci provided a shorter and more conceptual proof of a stre ngthened result that in addition to being CAT(0) establishes the completio n of the space of Riemannian metrics to depend only on the dimension of th e underlying manifold.\n\nAfter reviewing this recent progress\, I will pr esent new results providing a complete characterization of the Ebin metric 's self-isometries. Furthermore\, I will show that—in contrast to Cavall ucci's findings on the completion—the isometry class of the uncompleted space recovers the underlying manifold in the strongest plausible way.\n LOCATION:https://researchseminars.org/talk/VSGS/124/ END:VEVENT END:VCALENDAR