2003/06/20 by Nikita A. Nekrasov
Physics and Astronomy · #hep-th
published as Proceedings of the ICM, Beijing 2002, vol. 3, 477--496 · These are lecture notes from the ICM that summarize hep-th/0206161
arxiv created 2003/06/20 · arxiv updated 2009/11/30
In my lecture I consider integrals over moduli spaces of supersymmetric gauge field configurations (instantons, Higgs bundles, torsion free sheaves). The applications are twofold: physical and mathematical; they involve supersymmetric quantum mechanics of D-particles in various dimensions, direct computation of the celebrated Seiberg-Witten prepotential, sum rules for the solutions of the Bethe ansatz equations and their relation to the Laumon's nilpotent cone. As a by-product we derive some combinatoric identities involving the sums over Young tableaux.