# 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.

nakajima@math.kyoto-u.ac.jp