In this talk, we derive a Bernstein type result for the specialLagrangian equation, namely, any global convex solution must be quadratic.In terms of minimal surfaces, the result says that any global minimalLagrangian graph with convex potential must be a hyper-plane.

We study the classical worm domain of several complex variables.We develop new results about the Bergman kernel and projection.

I will survey some known facts and open questions concerning the global properties of 3+1 dimensional spacetimes, with emphasis on the Cauchy problem. According to the BKL proposal generic singularities with non-stiff matter are space-like and oscillatory while in the presence of stiff matter or scalar fields the singularity is quiescent. I will discuss the picture that emerges from the BKL proposal and review some recent results on nonlinear stability and the Cauchy problem with rough initial data.