Almost sure well-posedness for the cubic nonlinear Schr\"{o}dinger equation in the super-critical regime on ${\text{TTT}}^d$, $d\ge 3$

In this paper we prove almost sure local well-posedness in both atomic spaces $X^s$ and Fourier restriction spaces $X^{s,b}$ for the cubic nonlinear Schr"odinger equation on ${\text{TTT}}^d$ ($d\ge 3$) in the super-critical regime.