Chip-firing, served three ways

Chip-firing asks a simple question: Given a group of people and

an initial integer distribution of dollars among the people including people

in debt, can we redistribute the money so that no one ends up in debt? This

simple question with its origins in combinatorics can be reformulated using

concepts from linear algebra, graph theory, and even divisors in Riemann

surfaces. In this expository presentation, we will cover the original chip-

firing problem, along with three different approaches to solving this problem:

utilizing the Laplacian, Dhar’s algorithm, and a graph-theoretic version of

the Riemann-Roch theorem by Baker and Norine.

Georgia Institute of Technology College of Sciences