Ricci flow on Kaehler manifolds
  In this paper, we announce the following results: Let M be a Kaehler-Einstein manifold with positive scalar curvature. If the initial metric has nonnegative bisectional curvature and positive at least at one point, then the K\"ahler-Ricci flow converges exponentially fast to a Kaehler-Einstein metric with constant bisectional curvature. 
Xiuxiong Chen (Princeton University) and Gang Tian (MIT)