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SUMMARY:Introduction to K-stability - Michael Hallam (Oxford)
DTSTART:20191101T160000Z
DTEND:20191101T170000Z
UID:TALK133462@talks.cam.ac.uk
CONTACT:Nils Prigge
DESCRIPTION: Much of Riemannian geometry and geometric analysis centres on
  finding a ``best possible" metric on a fixed smooth compact manifold. One
  very nice metric on a compact complex manifold that we could ask for is a
  Kahler-Einstien metric\, the study of which goes back to the 50's with th
 e Calabi conjecture. For compact Kahler manifolds with non-positive first 
 chern class\, these were proven to always exist by Aubin and Yau in the 70
 's. However\, the case of positive first chern class is much more delicate
 \, and there are non-trivial obstructions to existence. It wasn't until th
 is decade that a complete abstract characterisation of Kahler-Einstein met
 rics became available\, in the form of K-stability. This is an algebro-geo
 metric stability condition\, whose equivalence to the existence of a Kahle
 r-Einstein metric in the Fano case is analogous to the Hitchin-Kobayashi c
 orrespondence for vector bundles. In this talk\, I will cover the definiti
 on of K-stability\, its relation to Kahler-Einstein (and more generally ex
 tremal) metrics\, and give some examples of how K-stability is calculated 
 in practice.
LOCATION:MR13
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