Kahler-type symplectic embeddings of balls into symplectic manifolds

Symplectic embeddings of balls into symplectic manifolds have been extensively studied since the famous non-squeezing theorem of Gromov (1985). However, even for basic closed symplectic manifolds, such as a complex projective space of real dimension 6 or higher, the classification of these embeddings up to a symplectomorphism of the target manifold is still unknown. I’ll discuss such a classification for a special kind of symplectic embeddings of balls - the so-called Kahler-type embeddings - that can be studied using complex geometry.

This is a joint work with M.Verbitsky.