# Natalie J. Durgin

Harvey Mudd College Mathematics 2009

Final Thesis: | Final Report: The Abelian Sandple Model on Symmetric Graphs |
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Thesis Proposal: | The Abelian Sandpile Model and the Symmetric Sandpile Subgroup |

Thesis Advisor: | Professor Francis Edward Su |

Second Reader: | Professor David Perkinson (Reed College) |

Thesis Talks: | HMC midyear talk, Fall 2008
PCUM conference, Spring 2009 |

## Abelian Sandpile Model and Symmetric Sandpile Subgroups

The abelian sandpile model, or chip-firing game, is a cellular automaton model on finite directed graphs often used to describe the phenomenon of self-organized criticality. Here we define the notion of a symmetric sandpile configuration, and show that such configurations form a subgroup of the sandpile group. Using these constructions, we explore various properties of this symmetric sandpile subgroup.