Instanton counting and non-abelian localization
-- Johan Martens

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Nekrasov has shown how the low-energy behaviour of certain
super-symmetric quantum field theories can be derived from
calculating equivariant volumes of moduli-spaces of instantons.
We review this and related recent work, and then sketch an
alternative method in symplectic geometry for calculating the
equivariant volumes, using varying compactifications of the
ADHM spaces and the Jeffrey-Kirwan-Witten method of non-abelian
localization. The advantage of this method is that it does not
require smoothness of the moduli-spaces, and is therefore very
suited for calculations on the moduli-spaces for classical
gauge groups other then SU(n).