Georgia Institute of Technology College of Sciences

I will discuss a natural elliptic obstacle problem that arises in the study of the Abelian sandpile. The Abelian sandpile is a deterministic growth model from statistical physics which produces beautiful fractal-like images. In recent joint work with Wesley Pegden, we characterize the continuum limit of the sandpile processusing PDE techniques. In follow up work with Lionel Levine and Wesley Pegden, we partially describe the fractal structure of the stable sandpiles via a careful analysis of the limiting obstacle problem.