Talk page
Title:
Symplectic packing stability beyond four dimensions
Speaker:
Abstract:
A classical question in symplectic geometry is to decide if a symplectic manifold can be symplectically fully filled by any large enough number of balls. A first answer was provided by P. Biran in the case of 4-dimensional manifolds with cohomologically rational symplectic forms. In collaboration with R. Hind we showed that this is also the case for all manifolds with rational cohomology class, for all compact 4-manifolds, and for several other symplectic domains (the latter two cases are based on joint work with R. Hind and E. Opshtein). I will explain how this phenomenon arises as an application of ECH, allowing one to show that rescalings of all sufficiently elongated ellipsoids (of "thin shape") can fully fill symplectic manifolds with rational cohomology class. Time permitting I will discuss how to further employ properties of ECH to probe the question of whether such behavior can be extended to other situations.
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