Global well--posedness for the mass--critical nonlinear Schr{ö}dinger equation on $\mathbb{T}$

Benjamin Dodson

We prove a global well--posedness result for the quintic NLS on $\mathbb{T}$ for initial data in $H^s(\mathbb{T})$, $s>1/3$. This improves the previous best bound of $s>2/5$.