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Random Tropical Curves

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.

Identiferoai:union.ndltd.org:CLAREMONT/oai:scholarship.claremont.edu:hmc_theses-1110
Date01 January 2017
CreatorsHlavacek, Magda L
PublisherScholarship @ Claremont
Source SetsClaremont Colleges
Detected LanguageEnglish
Typetext
Formatapplication/pdf
SourceHMC Senior Theses
Rights© 2017 Magda L Hlavacek, default

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