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J. Zachary Gaslowitz

Picture of J. Zachary Gaslowitz.

Thesis

Chip Firing Games and Riemann-Roch Properties for Directed Graphs

Advisor
Dagan Karp
Second Reader(s)
Dustin Cartwright

Abstract

The following presents a brief introduction to tropical geometry, especially tropical curves, and explains a connection to graph theory. We also give a brief summary of the Riemann-Roch property for graphs, established by Baker and Norine (2007), as well as the tools used in their proof. Various generalizations are described, including a more thorough description of the extension to strongly connected directed graphs by Asadi and Backman (2011). Building from their constructions, an algorithm to determine if a directed graph has Row Riemann-Roch Property is given and thoroughly explained.

Proposal

Tropical Riemann-Roch

Additional Materials

Poster