Symmetries related to Okounkov bodies

Add 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-Ampère 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
• All Talks (aka the CURE list)
• CMS Events
• DPMMS Lists
• DPMMS info aggregator
• DPMMS lists
• Hanchen DaDaDash
• Interested Talks
• MR2
• School of Physical Sciences
• bld31

Note that ex-directory lists are not shown.