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Michael Hutchings

Symplectic embeddings of cubes
星期四, 30 三月, 2017 - 16:3017:30

A symplectic embedding of one domain in R^(2n) into another is a smooth embedding which preserves the standard symplectic form. It is a fundamental problem to determine when one domain can be symplectically embedded into another. Even for simple domains such as ellipsoids and polydisks, this is a difficult question, and the known answers often involve subtle combinatorics. In general, one can obstruct the existence of symplectic embeddings using various “symplectic capacities”. We introduce a new series of symplectic capacities based on positive S^1-equivariant symplectic homology. These capacities can be computed combinatorially for “toric domains”, and lead to some sharp obstructions to symplectic embeddings in which the domain is a cube. Joint work with Jean Gutt.

University of California, Berkeley
Salle 4
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