  We establish global well-posedness and scattering for solutions to the
mass-critical nonlinear Schr\"odinger equation $iu_t + \Delta u = \pm |u|^{4/d}
u$ for large spherically symmetric L^2_x(R^d) initial data in dimensions $d\geq
3$. In the focusing case we require that the mass is strictly less than that of
the ground state. As a consequence, we obtain that in the focusing case, any
spherically symmetric blowup solution must concentrate at least the mass of the
ground state at the blowup time.

Analysis of PDEs