Aaron (Nung Kwan) Yip Purdue University Mathematics We study the surface diffusion of the boundary of a planar polygonal domain in the setting of crystalline surface energy. It is a motion law which mimics the evolution of a surface in which the surface normal velocity equals the Laplacian of mean curvature. This is a very common model for grain boundary growth. In contrast to the second order motion law -- motion by mean curvature, much less is known for the four-order surface diffusion case. We will characterize the velocity in the framework of canonical restriction and study its properties. In particular, the phenomena of splitting of a surface is analyzed.