Abstract:
In this talk we shall discuss infinite dimensional generalization of
Gromov's sympelctic nonsqueezing result. As an application we will present
mass subcritical and critical nonlinear Schrodinger equation. Nonsqueezing
property of the said flows was already known, however the techniques used
are based on finite dimensional Gromov's result, while ours presents a
more natural way of looking at the infinite dimensional Hamiltonian
structure of the equations. Additionally, we shall remark on future
projects in terms of application of the non-squeezing property. Joint work
with Herbert Koch.