  We study the connection between N = 2 supersymmetric gauge theories, quantum
cohomology and quantum integrable systems of hydrodynamic type. We consider
gauge theories on ALE spaces of A and D-type and discuss how they describe the
quantum cohomology of the corresponding Nakajima's quiver varieties. We also
discuss how the exact evaluation of local BPS observables in the gauge theory
can be used to calculate the spectrum of quantum Hamiltonians of spin Calogero
integrable systems and spin Intermediate Long Wave hydrodynamics. This is
explicitly obtained by a Bethe Ansatz Equation provided by the quiver gauge
theory in terms of its adjacency matrix.
