Sharp ellipsoid embeddings and almost-toric mutations

Abstract: We will show how to construct volume filling ellipsoid embeddings in some $4$-dimensional toric domain using mutations of almost toric compactifications of those. In particular we recover the results of McDuff-Schlenk for the ball, Fenkel-Müller for 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.

algebraic geometrycombinatorics

Audience: researchers in the topic

( slides | video )

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Online Nottingham algebraic geometry seminar

Series comments: Online geometry seminar, typically held on Thursday. This seminar takes place online via Microsoft Teams on the Nottingham University "Algebraic Geometry" team.

For recordings of past talks, copies of the speaker's slides, or to be added to the Team, please visit the seminar homepage at: kasprzyk.work/seminars/ag.html

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