Online Talk 

Liouville conformal field theory is a 2 dimensional conformal field theory corresponding to random surfaces. It was introduced in physics in the 80’s and studied using representation theory and algebraic methods but was not understood at the mathematical level. We shall explain how to construct it using probability through a mathematical definition of the path integral, and show how to obtain expressions for the correlation functions using analytic methods and by proving the so-called Segal axioms in this setting. This amounts to a spectral analysis of a Hamiltonian in infinite dimension with a singular potential. This gives a complete resolution of the theory. This is joint work with Kupiainen, Rhodes and Vargas.