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.