Abstract: I will discuss a local regularity theorem for totally real submanifolds of Kahler-Einstein manifolds. During the talk I will try to highlight similarities and differences between the mean curvature flow in the Lagrangian or totally real setting and the normalized Kahler-Ricci flow in the Fano setting. In particular, I will try to explain some similarities between the local regularity theorem and work of Phong-Sturm on convergence of the Kahler-Ricci flow and jumping of complex structures. This is joint with with A. Jacob, and Y.-S. Lin.