Explicit formulas and global uniqueness for phaseless inverse scattering in multidimensions

We consider phaseless inverse scattering for the Schr"odinger equation with compactly supported potential in dimension $d\ge 2$. We give explicit formulas for solving this problem from appropriate data at high energies. As a corollary, we give also a global uniqueness result for this problem with appropriate data on a fixed energy neighborhood.