Abstract

Nekrasov instanton partition function of 4d N=2 supersymmetric gauge theories is deeply connected to the integrability in the physics context, and thus is also deeply related to exact analysis in mathematics such as the resurgence. In this talk, I will first briefly give a review on the relation between supersymmetric gauge theories and a family of differential equations, the Heun equations. Then I will give two concrete examples, the charged C-metric and dS black hole, to show how this intriguing connection helps to solve an important class of physical quantities, called the quasinormal modes of black holes.