Title: Fibonacci Sumsets and the Gonality of Strip Graphs

Abstract:

Chip Firing is a game on graphs which establishes analogs between graph theory and algebraic geometry. We provide a new perspective on the divisor theory of graphs, using additive combinatorics. As a test case for this perspective, we compute the gonality of certain families of outerplanar graphs, specifically the strip graphs. These graphs give rise to additive sumsets consisting of fibonacci numbers. We shall provide the background to understanding gonality and then showcase our approach.