Continuity of the SLE trace in simply connected domains
  We prove that the $SLE_\kappa$ trace in any simply connected domain $G$ is continuous (except possibly near its endpoints) if $\kappa<8$. We also prove an SLE analog of Makarov's Theorem about the support of harmonic measure. 
Christophe Garban, Steffen Rohde, Oded Schramm