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SUMMARY:Michael Singer (University College London)
DTSTART:20200519T153000Z
DTEND:20200519T163000Z
DTSTAMP:20260423T022632Z
UID:Geolis/2
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/Geolis/2/">A
  construction of $D_k$ asymptotically locally flat gravitational instanton
 s from Atiyah-Hitchin and Taub-NUT geometries</a>\nby Michael Singer (Univ
 ersity College London) as part of Geometria em Lisboa (IST)\n\n\nAbstract\
 nComplete hyperKaehler 4-manifolds with cubic volume growth (and suitable 
 decay of the curvature)\, also known as ALF gravitational instantons\, are
  known to come in two families\, according to the `fundamental group at in
 finity’. This group must be a finite subgroup of $SU(2)$ and the only po
 ssibilities compatible with cubic volume growth are the cyclic groups ($A_
 k$) and binary dihedral groups ($D_k$).\n\nThis talk will be about the con
 struction of $D_k$ ALF gravitational instantons by a gluing construction i
 n which the ingredients are the moduli space of centred charge-2 monopoles
  ($D_0$) and a particularly symmetric\, but singular\, $A_k$ ALF gravitati
 onal instanton. This construction was suggested in a paper of Sen (1997). 
 It is also closely related to a construction due to Foscolo\, in which hyp
 erKaehler metrics are constructed on the $K3$ manifold that are `nearly’
  collapsed to a 3-dimensional space.\n\nThis is joint work with Bernd Schr
 oers.\n
LOCATION:https://researchseminars.org/talk/Geolis/2/
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