Abstract: The simplest kind of singularities that we expect along the Lagrangian mean curvature flow is those with tangent flow given by two transverse planes. I will talk about joint work with Jason Lotay and Felix Schulze, in which we show that such tangent flows are unique in the 2-dimensional case. It follows that the flow can be continued past the singularity, and in addition such singularities must be modeled on shrinking Lawlor necks.