The uniform spanning tree in two dimensions and its scaling limit.
The uniform spanning tree (UST) has played a major role in
recent developments in probability. The study of its scaling
limit led to the discovery of SLE by Oded Schramm.
In this talk I will discuss the geometry of the UST in
2 dimensions, and what we can say about its scaling limit,
This is joint work with David Croydon and Takashi Kumagai.