Pseudoholomorphic discs and symplectic structures in Hilbert space
  We develop the theory of $J$-holomorphic discs in Hilbert spaces with almost complex structures. As an aplication, we prove a version of Gromov's symplectic non-squeezing theorem for Hilbert spaces. It can be applied to short-time symplectic flows of a wide class of Hamiltonian PDEs. 
Alexandre Sukhov and Alexander Tumanov
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