  In this paper we obtain sharp obstructions to the symplectic embedding of the
lagrangian bidisk into four-dimensional balls, ellipsoids and symplectic
polydisks. We prove, in fact, that the interior of the lagrangian bidisk is
symplectomorphic to a concave toric domain using ideas that come from billiards
on a round disk. In particular, we answer a question of Ostrover. We also
obtain sharp obstructions to some embeddings of ellipsoids into the lagrangian
bidisk.
