The ellipsoid embedding function of a symplectic manifold measures the amount by which the symplectic form must be scaled in order to fit an ellipsoid of a given eccentricity. It generalizes the Gromov width and ball packing numbers. In 2012 McDuff and Schlenk computed the ellipsoid embedding function of the ball, showing that it exhibits a delicate piecewise linear pattern known as an infinite staircase. Since then, the embedding function of many other symplectic four-manifolds have been studied, and not all have infinite staircases. We will classify those symplectic Hirzebruch surfaces whose embedding functions have an infinite staircase, and explain how our work provides a blueprint for other targets. Based on work with Magill and McDuff and work in progress with Magill and Pires.
By Mélanie Bertelson
By Jean-Paul Mohsen
By Mohammed Abouzaid
By Ailsa Keating
By Daniel Alvarez-Gavela
By Kyler Siegel
By András Stipsicz
By Ko Honda
By Yu Pan
By Oleg Lazarev
By Paul Biran
By Ana Rechtman
By Albert Schwarz
By Albert Schwarz
By Juan Camilo Arosemena Serrato
By Pieter Spaas
By Francesca Arici
By Amine Marrakchi
