Infinite staircases in symplectic embedding capacity functions

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• Ana Rita Pires, Cambridge
• Wednesday 01 November 2017, 16:00-17:00
• MR13.

If you have a question about this talk, please contact Ivan Smith.

McDuff and Schlenk studied an embedding capacity function, which describes when a 4-dimensional ellipsoid can symplectically embed into a 4-ball. The graph of this function includes an infinite staircase related to the odd index Fibonacci numbers. Infinite staircases have been shown to exist also in the graphs of the embedding capacity functions when the target manifold is a polydisk or the ellipsoid E(2,3). I will describe how we use ECH capacities, lattice point counts and Ehrhart theory to show that infinite staircases exist for these and a few other target manifolds, as well as to conjecture that these are the only such target manifolds. This is a joint work with Cristofaro-Gardiner, Holm and Mandini.

This talk is part of the Differential Geometry and Topology Seminar series.

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