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In this paper we obtain sharp obstructions to the symplectic embedding of thelagrangian bidisk into four-dimensional balls, ellipsoids and symplecticpolydisks. We prove, in fact, that the interior of the lagrangian bidisk issymplectomorphic to a concave toric domain using ideas that come from billiardson a round disk. In particular, we answer a question of Ostrover. We alsoobtain sharp obstructions to some embeddings of ellipsoids into the lagrangianbidisk.

Symplectic embeddings and the lagrangian bidisk