This paper presents the lecture notes of a course that I taught at the Ninth Modave Summer School in Mathematical Physics. The course has been designed to give an introduction to new exact results for supersymmetric field theories obtained by localisation of the path integral. I first review localisation theorems for ordinary integrals and the extension of these ideas to supersymmetric quantum field theories. Then I introduce the formalism of rigid supersymmetry in curved space and apply it to three-dimensional N = 2 supersymmetric gauge theories on the round 3-sphere. Finally I sketch the derivation of the localisation formula for the partition functions of such theories.
Cremonesi, S. (2013). An Introduction to Localisation and Supersymmetry in Curved Space. Proceedings of Science, Modave2013,