Random Tropical Curves

• Main Author: Hlavacek, Magda L
• Format: Others
• Published: Scholarship @ Claremont 2017
• Subjects: tropical geometry; 14T05; Algebraic Geometry; Discrete Mathematics and Combinatorics
• Online Access: http://scholarship.claremont.edu/hmc_theses/95; http://scholarship.claremont.edu/cgi/viewcontent.cgi?article=1110&context=hmc_theses

In the setting of tropical mathematics, geometric objects are rich with inherent combinatorial structure. For example, each polynomial $p(x,y)$ in the tropical setting corresponds to a tropical curve; these tropical curves correspond to unbounded graphs embedded in $\R^2$. Each of these graphs is dual to a particular subdivision of its Newton polytope; we classify tropical curves by combinatorial type based on these corresponding subdivisions. In this thesis, we aim to gain an understanding of the likeliness of the combinatorial type of a randomly chosen tropical curve by using methods from polytope geometry. We focus on tropical curves corresponding to quadratics, but we hope to expand our exploration to higher degree polynomials.