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SUMMARY:Okounkov bodies\, moment maps and geodesics of Kahler metrics - Ju
 lius Ross (Cambridge)
DTSTART:20111130T141500Z
DTEND:20111130T151500Z
UID:TALK34085@talks.cam.ac.uk
CONTACT:Burt Totaro
DESCRIPTION:The Okounkov body can be thought of as an generalisation of th
 e\npolytope associated to a projective toric variety.  Starting with a lin
 e\nbundle L on an n-dimensional variety X and a flag of smooth subvarietie
 s\nin X\, the Okounkov body is a convex subset Delta in R^n\, whose volume
 \n(with respect to the Lebesgue measure) is the volume of X (with respect 
 to\nthe line bundle L).  This property forms the basis of work by\nLazarsf
 eld-Mustata who use Okounkov bodies to study the volume functional\non the
  space of big divisors.\n\nIn this talk I will start with a general discus
 sion of Okounkov bodies\,\nalong with some examples.  I shall then describ
 e ongoing (and very\nunfinished) work with David Witt-Nystrom which attemp
 ts to construct a\nversion of the moment map in this setting.
LOCATION:MR13\, CMS
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