Squeezing the symplectic ball (up to a subset)

Abstract: In a recent preprint, Sackel-Song-Varolgunes-Zhu investigate quantitative questions surrounding Gromov's non-squeezing theorem. In particular, they show that if one can embed the four-ball into a cylinder of smaller capacity after the removal of a subset, then this subset has Minkowski dimension at least two. Furthermore, they give an explicit example of such a "squeezing up to a subset" where the subset they remove has dimension two and allows squeezing by a factor of two (in terms of capacities). In this talk, we will discuss certain squeezings by a factor of up to three. The construction is inspired by degenerations of the complex projective plane and almost toric fibrations. If time permits, we will give a construction by hand and discuss how this leads to a different viewpoint on almost toric fibrations and potential squeezings in higher dimensions. This is partially based on work that will appear as an appendix of the SSVZ paper.

differential geometrydynamical systemsgeometric topologysymplectic geometry

Audience: researchers in the topic

Geometry and Dynamics seminar

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