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Section de mathématiques
 Université de Genève

Mathematical Physics: from XX to XXI century

in honor of the 75th birthday of Ludwig Faddeev


Nikita Nekrasov, "Supersymmetric vacua, quantum cohomology, and Bethe ansatz"

The equivariant quantum cohomology, K-theory, and elliptic cohomology of various hyperkahler quotients are identified with the quantum integrable systems, such as spin chains or many-body systems. In particular, the cotangent bundle to the Grassmanian is mapped to the Heisenberg magnet.
The spectrum of the operators of quantum multiplication is identified with the solutions of the Bethe equations.
The generalized Donaldson theory on the product of a two-sphere and a Riemann surface lead to the instanton corrected Bethe equations.

Based on the joint work with S. Shatashvili