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We consider the problem of large data scattering for the quintic nonlinearSchr\"odinger equation on $\R \times \T^2$. This equation is critical both atthe level of energy and mass. Most notably, we exhibit a new type of profile (a"large scale profile") that controls the asymptotic behavior of the solutions.

On scattering for the quintic defocusing nonlinear Schr\"odinger equation on \R \times \T^2