We discuss the shape invariant, a sort of set valued symplectic capacity defined by the Lagrangian tori inside a domain of ℝ4. Partial computations for convex toric domains are sometimes enough to give sharp obstructions to symplectic embeddings, but in general the shape is far from a complete invariant. We then consider continuous families of Lagrangian embeddings, and describe a seemingly close relation to stabilized symplectic embeddings.
This is ongoing work with Ely Kerman and Jun Zhang.
This video is part of the Institute for Advanced Study‘s Symplectic geometry seminar.
