Singularities of Lagrangian mean curvature flow

We study singularities of Lagrangian mean curvature flow in Cn when the initial condition is a zero-Maslov class Lagrangian. We show that under these conditions the rescaled flow at a singularity converges weakly to a finite union of area-minimizing Lagrangian cones. Under the additional assumptions that the initial condition is an almost-calibrated and rational Lagrangian we show that, on each connected component of the rescaled flow, the Lagrangian angle converges to a single constant. Explicit examples of finite time singularities are given, including a Lagrangian which is Hamiltonian isotopic to a plane but develops a finite time singularity under mean curvature flow.