Symplectic embeddings from concave toric domains into convex ones

Joint Columbia-IAS-Princeton Symplectic Seminar
Topic:Symplectic embeddings from concave toric domains into convex ones
Speaker:Dan Cristofaro-Gardiner
Affiliation:Harvard University
Date:Friday, October 24
Time/Room:11:00am - 12:00pm/S-101
Video Link:http://video.ias.edu/jointcip/2014/1024-DanCristofaroGardiner

Embedded contact homology gives a sequence of obstructions to four-dimensional 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.