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.