  We determine the ring structure of the equivariant quantum cohomology of the
Hilbert scheme of points in the complex plane. The operator of quantum
multiplication by the divisor class is a nonstationary deformation of the
quantum Calogero-Sutherland many-body system. A relationship between the
quantum cohomology of the Hilbert scheme and the Gromov-Witten/Donaldson-Thomas
correspondence for local curves is proven.
