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SUMMARY:Index-energy estimates for Yang-Mills connections and Einstein met
 rics - Casey Kelleher (Princeton University)
DTSTART:20190304T160000Z
DTEND:20190304T170000Z
UID:TALK120331@talks.cam.ac.uk
CONTACT:Prof. Mihalis Dafermos
DESCRIPTION:We prove a conformally invariant estimate for the index of Sch
 rödinger operators acting on vector bundles over four-manifolds\, related
  to the classical Cwikel-Lieb-Rozenblum estimate. Applied to Yang-Mills co
 nnections we obtain a bound for the index in terms of its energy which is 
 conformally invariant\, and captures the sharp growth rate. Furthermore we
  derive an index estimate for Einstein metrics in terms of the topology an
 d the Einstein-Hilbert energy. Lastly we derive conformally invariant esti
 mates for the Betti numbers of an oriented four-manifold with positive sca
 lar curvature. This is joint work with Matthew Gursky and Jeffrey Streets.
LOCATION:CMS\, MR13
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