## Oliver Club

What is a natural way to choose a two-dimensional surface at random and what does such a random surface look like ? This question dates back to Polyakov's landmark 1981 paper “Quantum geometry of bosonic strings” and has since undergone extensive study in probability theory. In this talk we will first explain how to construct these models of random surfaces using the Gaussian free field and present several of their properties, including the laws of random lengths, areas, and of the random moduli of an annulus. In a second part we will connect random surfaces with conformal field theory, the physics framework that allows to use the conformal symmetries of the theory to perform many explicit computations. Based on joint work with M. Ang, P. Ghosal, X. Sun, Y. Sun, and T. Zhu.