Abstract：

In this talk we will discuss the O(n) loop model on quadrangulations. We will first introduce the model, its basic properties and several related work for preliminaries. Then we discuss the volume of maps and state our scaling limit result for the volume of the O(n) quadrangulations. In the end, we will state the outline of our proof and some observations of the relationship with branching random walk. This talk is based on joint work with Élie Aïdékon (Fudan University) and William Da Silva (University of Vienna).