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

We consider the problem of large data scattering for the quintic nonlinear Schr"odinger equation on $\mathbb{R}\times {\text{T}}^2$. This equation is critical both at the 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.