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Magda Hlavacek

Picture of Magda Hlavacek.

Thesis

Random Tropical Curves

Advisor
Dagan Karp
Second Reader(s)
Meldoy Chan (Brown University)

Abstract

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 $\mathbb{R}^2$. 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.

Additional Materials

Poster