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University of Cambridge > Talks.cam > Workshop on Kahler Geometry > Symmetries related to Okounkov bodies

## Symmetries related to Okounkov bodiesAdd to your list(s) Download to your calendar using vCal - David Witt-Nystrom (Chalmers University)
- Wednesday 11 April 2012, 16:00-17:00
- MR2.
If you have a question about this talk, please contact Dr. J Ross. I will discuss some joint work with Julius Ross. In toric geometry, line bundles are associated with polytopes. In 1996 Andrei Okounkov found a way to generalize this, so that any ample line bundle L gets an associated convex body, called the Okounkov body. However, while the toric construction encodes the symplectic geometry of the variety, Okounkov’s construction is of a purely algebro-geometric nature. We wonder if there is a corresponding symplectic interpretation of the Okounkov body, involving the symplectic form defined by the curvature form of a fixed metric on L, as there is in the toric case? By setting up a certain homogeneous Monge-AmpĂ¨re equation, we show that we can accomplish this, given some regularity assumptions on the solutions to the HMAE . In one dimension the problem is equivalent to finding a solution to the Hele-Shaw flow. Recall that this flow describes the propagation of a fluid being injected in between two plates that are close to each other. This talk is part of the Workshop on Kahler Geometry series. ## This talk is included in these lists:- All CMS events
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