Conformal symmetry is one of the most powerful tools in physics, providing a means to perform numerous computations and investigate an extensive range of physical systems from ferromagnets to black holes. But what are exactly these conformal symmetries and how do they arise?
In this talk, starting from the statistical physics example of the Ising model, I will show how conformal symmetries can emerge. I will then explain more precisely what conformal invariance entails for a physical system and how it can lead to simpler computations. Finally, I will present examples of applications of conformal symmetries beyond statistical physics such as the renowned AdS/CFT correspondence.