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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