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UID:8fa81bdf668f502c5f31a22aee3dbf0e
CATEGORIES:Topology/Geometry Seminar
CREATED:20211005T101402
SUMMARY:Collapsing geometry of hyperkaehler four-manifolds
LOCATION:Hill Center room 525
DESCRIPTION:<p>Abstract:&nbsp;This talk focuses on the recent resolution of two well-kn
 own conjectures in the study of Ricci-flat four manifolds (joint with Song 
 Sun).</p><p>(1) Any volume collapsed limit of unit-diameter hyperkaehler me
 trics on the K3 manifold is isometric to one of the following: the quotient
  of a flat 3-torus by an involution, a singular special Kaehler metric on t
 he 2-sphere, or the unit interval.</p><p>(2) Any complete hyperkaehler 4-ma
 nifold with quadratically integrable curvature must have one of the followi
 ng asymptotic model geometries: ALE, ALF, ALG, ALH, ALG* and ALH*.</p><p>Co
 mbining with known results, we have obtained a rather complete picture of c
 ollapsing hyperkaehler metrics bounded curvature energy in real dimension f
 our (Gromov-Hausdorff limits, rescaling limits, bubble tree structure, etc)
 .</p>
CONTACT:Ruobing Zhang (Princeton University)
DTSTAMP:20260829T234717
DTSTART;TZID=America/New_York:20211012T110000
DTEND;TZID=America/New_York:20211012T120000
SEQUENCE:0
TRANSP:OPAQUE
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