BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Jiayin Pan (University of California-Santa Barbara) DTSTART:20210407T220000Z DTEND:20210407T230000Z DTSTAMP:20260423T052930Z UID:VSGS/25 DESCRIPTION:Title: No nnegative Ricci curvature\, escape rate\, and virtual abelianness\nby Jiayin Pan (University of California-Santa Barbara) as part of Virtual sem inar on geometry with symmetries\n\n\nAbstract\nA consequence of Cheeger-G romoll splitting theorem states that for any open manifold $(M\,x)$ of non negative Ricci curvature\, if all the minimal geodesic loops at $x$ that r epresent elements of $\\pi_1(M\,x)$ are contained in a bounded set\, then $\\pi_1(M\,x)$ is virtually abelian. However\, it is prevalent for these l oops to escape from any bounded sets. In this talk\, we introduce a quanti ty\, escape rate\, to measure how fast these loops escape. Then we prove t hat if the escape rate is less than some positive constant $\\epsilon(n)$\ , which only depends on the dimension $n$\, then $\\pi_1(M\,x)$ is virtual ly abelian. The main tools are equivariant Gromov-Hausdorff convergence an d Cheeger-Colding theory on Ricci limit spaces.\n LOCATION:https://researchseminars.org/talk/VSGS/25/ END:VEVENT END:VCALENDAR