Abstract:  Originating in statistical physics and nearly simultaneously and independently introduced in algebraic graph theory and in theoretical computer science in the 1990s, the Abelian Sandpile Model associates a variety of structures with a diffusion process on finite graphs.  The model gives rise to a remarkably rich theory which connects the fields of graph theory, stochastic processes, commutative semigroups and groups, matrices and determinants, lattices in n-dimensional space, algorithms, number theory, discrete dynamical syetems, and more.

After a general introduction, I will outline work I have done recently with then undergraduate Igor Gorodezky; the collaboration started at a summer REU.