Abstracts
for the Seminar

Spring 2019

**Speaker: **David Perkinson, Reed College and MIT

**Title: **Enumerating Linear Systems on Graphs

**Time:** 2:30 PM, Monday, April 22, 2019

**Place:** Malott 206

**Abstract:** To play the dollar game on a graph, start by assigning to each vertex a number of dollars of either wealth or debt. From this initial state, called a "divisor", the vertices lend and borrow with their neighbors according to chip-firing rules in an attempt to reach a debt-free state. The set of all possible winning states is the "complete linear system" of the divisor. We are interested in determining its cardinality. This is joint work with Sarah Brauner and Forrest Glebe.

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