The conformal continuum random tree
The Continuum Random Tree, introduced by Aldous in the 90’s, arises in numerous
diﬀerent ways, for instance as the scaling limit of large uniform trees, via Brownian excursions, or
via a Poisson point processes. It carries a natural structure as a metric measure space and has
recently featured prominently in the LeGall’s and Miermont’s work on the Brownian map, as well
as Duplantier’s, Miller’s and Sheﬃeld’s Brownian sphere. Beginning from basic deﬁnitions, I will
describe some of the highlights of this emerging theory such as connections to Liouville Quantum
Gravity, and will describe how to draw the CRT in the plane in a conformally natural way.