Back To School Seminar: Mating of Continuum Random Trees

In this talk, I will introduce a probabilistic object called the continuum random tree (CRT). We will talk about how gluing two such trees together can help us model the quantum gravity in 2D. We will go through the definition of these random trees as well as their associated random process—Brownian excursion. Using the techniques from probability and topology, we will show why the gluing process of two CRTs produces a topological 2-sphere.