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SUMMARY:Symmetries related to Okounkov bodies - David Witt-Nystrom (Chalme
 rs University)
DTSTART:20120411T150000Z
DTEND:20120411T160000Z
UID:TALK36839@talks.cam.ac.uk
CONTACT:Dr. J Ross
DESCRIPTION:I will discuss some joint work with Julius Ross.\n\nIn toric g
 eometry\, line bundles are associated with polytopes. In 1996 Andrei Okoun
 kov found a way to generalize this\, so that any ample line bundle L gets 
 an associated convex body\, called the Okounkov body.\n\nHowever\, while t
 he toric construction encodes the symplectic geometry of the variety\,  Ok
 ounkov's construction is of a purely algebro-geometric nature. We wonder i
 f there is a corresponding symplectic interpretation of the Okounkov body\
 , involving the symplectic form defined by the curvature form of a fixed m
 etric on L\, as there is in the toric case?\n\nBy setting up a certain hom
 ogeneous Monge-Ampère equation\, we show that we can accomplish this\, gi
 ven some regularity assumptions on the solutions to the HMAE. In one dimen
 sion the problem is equivalent to finding a solution to the Hele-Shaw flow
 . Recall that this flow describes the propagation of a fluid being injecte
 d in between two plates that are close to each other.\n
LOCATION:MR2
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