MIT Symplectic Seminar

Building 2, 449

Speaker: Dan Cristofaro-Gardiner (University of Maryland)Title: On symplectic packing stabilityAbstract: The k-th "symplectic packing number" of a finite volume symplectic manifold is the proportion of the volume that can be filled by k disjoint symplectically embedded balls. In the 90s, Biran discovered the following remarkable stability phenomenon: for many symplectic manifolds, the packing number is 1 for sufficiently large k. I will explain some recent joint work aimed at understanding how characteristic packing stability actually is. The main topic will be the following. It has been conjectured that packing stability holds for all symplectic manifolds, but I will explain why it does not. Closely tied to our work is an old question, which asks to what extent an open symplectic-manifold has a well-defined boundary: we show that many examples for which packing stability fails can not be symplectomorphic to the interior of any compact symplectic manifold with smooth boundary. A "fractal Weyl law" plays a major role in our proofs. I also want to briefly survey some positive results about some new cases (e.g. closed symplectic 6-manifolds) for which packing stability does hold.