The Conformal Continuum Random Tree

I will begin with a gentle introduction to "conformal welding" from the probabilistic viewpoint, which is at the heart of Scott Sheffields "quantum zipper" as well as Malliavin's and his coauthors work on Brownian measures on the group of circle homeomorphisms. Then I will describe a conformal welding problem involving to the CRT, discuss the existence of its solution (joint work with Peter Lin), and describe how it arises as the limit of certain dessin d'enfants.