J. Zachary Gaslowitz
Harvey Mudd College Mathematics 2013
| Thesis Proposal: | Tropical Riemann-Roch |
|---|---|
| Thesis Advisor: | Prof. Dagan Karp |
| Second Reader: | Dustin Cartwright |
| E-Mail: | Zachary_Gaslowitz@hmc.edu |
Chip Firing Games and Riemann-Roch Properties for Directed Graphs
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 Matt Baker and Serguei Norine, 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 Arash Asadi and Spencer Backman. Building from their constructions, an algorithm to determine if a directed graph has Row Riemann-Roch Property is presented and explained.