The Mathematics of Chip-Firing

Caroline Klivans
Professor of Applied Mathematics, Deputy Director of ICERM
Brown University

Chip-firing processes are discrete dynamical systems. A commodity (chips, sand, dollars) is exchanged between sites of a network according to simple local rules. Although governed by local rules, the long-term global behavior of the system reveals unexpected properties, including intricate fractal-like patterns. In this talk, I will give a broad survey of the theory of chip-firing, highlighting both classical results and recent advances.