In-Person Talk 

In this talk I will introduce the notion of conformal field theory in dimension 2 using Segal’s approach. I will then focus on a particular case called Liouville conformal field theory that can be defined using probabilistic tools, and can be understood as a theory of random Riemannian metrics on surfaces. 

In a second time, I will explain how the algebra of symmetries, called Virasoro algebra, and the spectral resolution of a certain operator of this algebra allows to find expressions for the correlation functions of this theory in terms of universal functions on moduli space called conformal blocks.