Joint ColumbiaIASPrinceton Symplectic Seminar: Symplectic embeddings from concave toric domains into convex ones
Joint ColumbiaIASPrinceton Symplectic Seminar: Symplectic embeddings from concave toric domains into convex ones

Dan CristofaroGardiner , Harvard University
IAS Room S101
This is a Joint ColumbiaIASPrinceton Symplectic Seminar. Embedded contact homology gives a sequence of obstructions to fourdimensional symplectic embeddings, called ECH capacities. These obstructions are known to be sharp in several interesting cases, for example for symplectic embeddings of one ellipsoid into another. We explain why ECH capacities give a sharp obstruction to embedding any "concave toric domain" into a "convex" one. We also explain why the ECH capacities of any concave or convex toric domain are determined by the ECH capacities of a corresponding collection of balls. Some of this is joint work with Keon Choi, David Frenkel, Michael Hutchings, and Vinicius Ramos.