Charles K. Smart: The scaling limit of the Abelian sandpile on periodic graphs

Joint work with Lionel Levine and Wesley Pegden. The Abelian sandpile is a deterministic diffusion process on graphs which, at least on periodic planar graphs, generates striking fractal configurations. The scaling limit on the two dimensional integer lattice can be described in terms of an Apollonian circle packing. General periodic graphs share some of this structure, but appear to have more complicated scaling limits in general. I will discuss both the lattice and general cases.