Partition function N=(2,2) gauge theories on S^2 and vortices Seminar

I will review supersymmetry on curved space and localisation and apply these methods to compute partition functions of 2d N=(2,2) supersymmetric gauge theories with a vector U(1) R-symmetry on the round 2-sphere. Two alternative localisation schemes lead to complementary ``Coulomb branch'' and ``Higgs branch'' representations of the partition function. If time allows, I will briefly overview the potential of these exact results for the study of type II string compactifications, geometry and supersymmetric theories in various dimensions.