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Monday, February 9, 2015

**Abstract:** The celebrated Gromov's non-squeezing theorem of 1985 says that the unit ball $B^{2n}$ in $R^{2n}$ can be symplectically embedded in the "cylinder" $rB^2 \times R^{2n-2}$ of radius $r$ only if $r\ge 1$. I present a generalization of this theorem for Hilbert space. The result can be applied to symplectic flows of Hamiltonian PDEs. This work is joint with Alexander Sukhov.