Tatiana Smirnova-Nagnibeda: Criticality of the Abelian Sandpile Model on self-similar graphs

The abelian sandpile model (also known under the name of the chip-firing game on graphs) is a simple combinatorial model of a number of natural and social phenomena obeying to the rules of so-called self-organized criticality. Though there is a lot of physical evidence towards this type of behaviour, mathematical proofs are scarce. In this talk I will describe a family of graphs (coming from approximation of certain fractal sets, as Julia sets of quadratic polynomials) that allow for a rigorous analysis of the abelian sandpile model on them and lead to new examples of critical behaviour. All the notions involved will be explained in the talk.