We report recent advances in SLE (Schramm-Loewner evolution). SLE is defined by a differential equation in terms of Brownian motion, and was invented by Schramm in 2000. The theory exhibits an interplay between probability and complex analysis. 

 

In particular, we report results on Green’s function by G. Lawler, who will give a plenary lecture in the coming ICM. These results are related to, and can hopefully help us to accomplish, an ongoing project of us on the angular distribution of SLE.