Instanton counting and Donaldson invariants

Hiraku Nakajima (Kyoto)
Abstract : (based on joint work with L.Goettsche and K.Yoshioka) Nekrasov introduced a certain partition function, which can be regarded as the generating function of Donaldson invariants of $\mathbf R^4$ with the torus action. He conjectured that its leading coefficient is equal to the so-called Seiberg-Witten prepotential, which is defined via periods of elliptic curves. I will explain its solution and the relation to ordinary Donaldson invariants of 4-manifolds, especially to the wall-crossing formula.