Sharp Ellipsoid Embeddings and Toric Mutations

Abstract: We will show how to construct volume filling ellipsoid embeddings in some 4-dimensional toric domain using mutation of almost toric compactification of those. In particular we recover the results of McDuff-Schlenk for the ball, Fenkel-Müller for the product of symplectic disks and Cristofaro-Gardiner for E(2,3), giving a more explicit geometric perspective for these results. To be able to represent certain divisors, we develop the idea of symplectic tropical curves in almost toric fibrations, inspired by Mikhalkin's work for tropical curves. This is joint work with Roger Casals. Obs: The same result appears in "On infinite staircases in toric symplectic four-manifolds", by Cristofaro-Gardiner -- Holm -- Mandini -- Pires. Both papers were posted simultaneously on arXiv.

mathematical physicsalgebraic geometrysymplectic geometry

Audience: researchers in the topic

IBS-CGP weekly zoom seminar

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