MATH 435
Chip-firing Games on Graphs
Last Offered Fall 2021
Division III Quantitative/Formal Reasoning
This course is not offered in the current catalog

Starting with a graph (a collection of nodes connected by edges), place an integer number of poker chips on each vertex. Move these chips around according to “chip-firing moves”, where a vertex donates a chip along each edge. These simple and intuitive games quickly lead to challenging mathematics with applications ranging from dynamical systems to algebraic geometry. In this course we’ll build up a mathematical framework for studying chip-firing games, drawing on linear algebra and group theory. We’ll discover algorithms for winning these games, and study their complexity; and we’ll prove graph-theoretic versions of famous results like the Riemann-Roch theorem. A key component of this course will be research projects that draw on open questions about chip-firing.