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SUMMARY:Ruling out non-collapsed singularities in Riemannian 4-manifolds v
 ia the symplectic geometry of their twistor spaces - Fine\, J (Universit L
 ibre de Bruxelles)
DTSTART:20150723T130000Z
DTEND:20150723T140000Z
UID:TALK60186@talks.cam.ac.uk
CONTACT:42080
DESCRIPTION:The twistor space of a Riemannian 4-manifold carries a natural
  closed 2-form. Asking that it be symplectic gives an interesting curvatur
 e inequality (which includes\, for example\, anti-self-dual Einstein metri
 cs of non-zero scalar curvature). I will explain how the theory of J-holom
 orphic curves in the twistor space can be used to rule out certain types o
 f degeneration in families of manifolds satisfying the curvature inequalit
 y. In particular\, this shows that anti-self-dual Einstein metrics of nega
 tive scalar curvature cannot develop non-collapsed singularities. If there
  is time\, I will end with speculation about other Riemannian uses for the
 se symplectic structures and various conjectures concerning them. \n
LOCATION:Seminar Room 2\, Newton Institute Gatehouse
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