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CATEGORIES:Junior Geometry Seminar
SUMMARY:Introduction to K-stability - Michael Hallam (Oxfo
rd)
DTSTART;TZID=Europe/London:20191101T160000
DTEND;TZID=Europe/London:20191101T170000
UID:TALK133462AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/133462
DESCRIPTION: Much of Riemannian geometry and geometric analysi
s centres on finding a ``best possible" metric on
a fixed smooth compact manifold. One very nice met
ric on a compact complex manifold that we could as
k for is a Kahler-Einstien metric\, the study of w
hich goes back to the 50's with the Calabi conject
ure. For compact Kahler manifolds with non-positiv
e 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 de
licate\, and there are non-trivial obstructions to
existence. It wasn't until this decade that a com
plete abstract characterisation of Kahler-Einstein
metrics became available\, in the form of K-stabi
lity. This is an algebro-geometric stability condi
tion\, whose equivalence to the existence of a Kah
ler-Einstein metric in the Fano case is analogous
to the Hitchin-Kobayashi correspondence for vector
bundles. In this talk\, I will cover the definiti
on of K-stability\, its relation to Kahler-Einstei
n (and more generally extremal) metrics\, and give
some examples of how K-stability is calculated in
practice.
LOCATION:MR13
CONTACT:Nils Prigge
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