3/8/2006

Nikita Nekrasov
IHES

Instanton partition functions

Instantons are the finite action solutions of Euclidean equations of motion. The examples of instantons are holomorphic maps of Riemann surfaces, or anti-self-dual connections on principal bundles over four dimensional manifolds. In physics, the integrals over moduli spaces of instantons give an approximation to the correlation functions in quantum field or string theory. In certain supersymmetric models these approximations are exact. I will review the definitions of the instanton partition functions in two, four, and six dimensional theories, formulate several duality conjectures about them. In particular, I will explain how the proof of A.Okounkov and myself that the asymptotics of Nekrasov partition function is expressed in terms of Seiberg-Witten geometry can be recast in the context of mirror symmetry.