Global well-posedness and scattering for the defocusing cubic Schrödinger equation on waveguide R² × T²

We consider the problem of large data scattering for the defocusing cubic nonlinear Schrödinger equation on R² × T². This equation is critical both at the level of energy and mass. The key ingredients are global-in-time Stricharz estimate, resonant system approximation, profile decomposition and energy induction method. Assuming the large data scattering for the 2d cubic resonant system, we prove the large data scattering for this problem. This problem is the cubic analogue of a problem studied by Hani and Pausader.