BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Ruobing Zhang DTSTART:20211116T133000Z DTEND:20211116T143000Z DTSTAMP:20260423T004657Z UID:GeoSem/29 DESCRIPTION:Title: Collapsing geometry of hyperkaehler four-manifolds\nby Ruobing Zhang a s part of Geometry Seminar - University of Florence\n\n\nAbstract\nThis ta lk focuses on the recent resolution of the following three well-known conj ectures in the study of Ricci-flat four manifolds (joint with Song Sun). \ n\n(1) Any volume collapsed limit of unit-diameter hyperkaehler metrics on the K3 manifold is isometric to one of the following: the quotient of a f lat 3-torus by an involution\, a singular special Kaehler metric on the 2- sphere\, or the unit interval. \n(2) Any complete non-compact hyperkaehler 4-manifold with quadratically integrable curvature must have one of the f ollowing asymptotic model geometries: ALE\, ALF\, ALG\, ALH\, ALG* and ALH *.\n(3) Any gravitational instanton is holomorphic to an open dense subset of some compact algebraic surface.\n\nWith the above classification resul ts\, we obtain a rather complete picture of the collapsing geometry of hyp erkaehler four manifolds.\n LOCATION:https://researchseminars.org/talk/GeoSem/29/ END:VEVENT END:VCALENDAR