Quantum cohomology and quantum groups

We describe the recent research started by Nekrasov, Shatashvili, Braverman, Maulik, Okounkov on correspondence between the quantumcohomology of the quiver varieties and the quantum integrable systems. Our main example will be the quantum cohomology of the cotangent spaces to partial flag varieties and its vis a vis from the representation theory, the quasi periodic Heisenberg spin chain. We will discuss how the both subjects may contribute to each other via this correspondence.