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In this paper we prove that the defocusing, $d$-dimensional mass criticalnonlinear Schr{\"o}dinger initial value problem is globally well-posed andscattering for $u_{0} \in L^{2}(\mathbf{R}^{d})$ and $d \geq 3$. To do this, wewill prove a frequency localized interaction Morawetz estimate similar to theestimate made in [10]. Since we are considering an $L^{2}$ - critical initialvalue problem we will localize to low frequencies.

Global well-posedness and scattering for the defocusing, $L^{2}$-critical, nonlinear Schr{\"o}dinger equation when $d \geq 3$