Direct evaluation of the Seiberg-Witten prepotential is accomplished following the
localization programme suggested in [1]. Our results agree with all low-instanton …

We study N= 2 supersymmetric four-dimensional gauge theories, in a certain 525-02= 2
supergravity background, called the Ω-background. The partition function of the theory in the …

We analyze local operator growth in nonintegrable quantum many-body systems. A recently
introduced universal operator growth hypothesis proposes that the maximal growth of …

This Licentiate Thesis contains the following papers: 1. Ernst T., Silvestrov SD: Shift
difference equations, symmetric polynomials and representations of the symmetric group …

We give a mathematically rigorous proof of Nekrasov's conjecture: the integration in the
equivariant cohomology over the moduli spaces of instantons on ℝ 4 gives a deformation of …

We review the study of the relation between integrable many-body systems and gauge
theories. We show that the degrees of freedom of integrable systems are related to the …

These notes have two parts. The first is a study of Nekrasov's deformed partition functions $
Z (\ve_1,\ve_2,\vec {a};\q,\vec {\tau}) $ of N= 2 SUSY Yang-Mills theories, which are …

We present new evidence for the conjecture that BPS correlation functions in
supersymmetric gauge theories are described by an auxiliary two dimensional conformal …

Abstract We solve= 2 supersymmetric Yang-Mills theories for an arbitrary classical gauge
group, ie SU (N), SO (N), Sp (N). In particular, we derive the prepotential of the low-energy …

In the paper Int. J. Mod. Phys. A 19, 4127 (2004), we started a program of creating a
reference-book on matrix-model τ-functions, the new generation of special functions, which …