Speaker
Ralihe Raul Villagran Olivas
(Worcester Polytechnic Institute)
Description
Chip-firing is a discrete dynamical process on a graph that exhibits striking phenomena, including fractal-like symmetries and self-organized criticality. From an algebraic perspective, the states of this process (combinatorially) define a group, the Sandpile group, whose algebraic structure is given by the Smith normal form of the Laplacian matrix. We will discuss problems related to Sandpile Groups and introduce some determinantal ideals for graphs. We will discuss how these algebraic invariants provide a framework for solving said problems in graph theory and, conversely, how the structure of Sandpile groups offers new insights into the properties of these ideals.
Author
Ralihe Raul Villagran Olivas
(Worcester Polytechnic Institute)