Department of Mathematical Sciences
Discrete Math Seminar
Thursday, January 29th, 2026
12:00PM-12:50PM
Olin Hall 218
Speaker: Ralihe Raul Villagran Olivas, WPI
Title: Sandpile Groups: From Chip-Firing to Determinantal Ideals and Back
Abstract: 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. 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.