Event description
Abstract: Supersymmetry is a powerful tool to study QFT observables at the non-perturbative level and leads to deep connections between physics and geometry. In this talk, we will discuss some applications of equivariant cohomology in computing observables of 4d supersymmetric gauge theories. In the first part, we will review supersymmetric gauge theories and the topological twist construction of Witten and the Donaldson-Witten theory of invariants of 4-manifolds. We will then describe its equivariant extension for toric manifolds, which allows to compute the full non-perturbative partition function of the gauge theory, the so called Nekrasov partition function, as a sum over fixed points in the instanton moduli space. In the final part, we will discuss the Seiberg-Witten theory and its equivariant generalization in terms of quantum curves. We will also mention some interesting correspondences between Nekrasov functions, conformal blocks in 2d CFT, integrable systems and partition functions of topological string theory.