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SUMMARY:An analytic construction of dihedral ALF gravitational instantons 
 - Auvray\, H (Universit Paris-Sud)
DTSTART:20150727T103000Z
DTEND:20150727T113000Z
UID:TALK60210@talks.cam.ac.uk
CONTACT:42080
DESCRIPTION:Gravitational instantons are 4-dimensional complete non-compac
 t hyperkhler manifolds with some curvature decay at infinity. The asymptot
 ic geometry of these spaces plays an important role in a conjectural class
 ification\; for example\, instantons of euclidean\, i.e. quartic\, large b
 all volume growth\, are completely classified by Kronheimer\, whereas the 
 cubic regime\, i.e. the {it ALF (Asymptotically Locally Flat)} case\, is n
 ot fully understood yet. More precisely\, ALF instantons with {it cyclic t
 opology at infinity} are classified by Minerbe\; by contrast\, a classific
 ation in the {it dihedral} case at infinity is still unknown. \n\nA wide\,
  conjecturally exhaustive\, range of dihedral ALF instantons were construc
 ted by Cherkis-Kapustin\, adopting the moduli space point of view\, and st
 udied explicitly by Cherkis-Hitchin. I shall explain in this talk another 
 construction of such spaces\, based on the resolution of a Monge-Ampre equ
 ation in ALF geometry. \n
LOCATION:Seminar Room 1\, Newton Institute
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