WHEN: 29.01.15 at 14:15
WHERE: Seminar Room, Arnimallee 2, FU Berlin

Speaker: Sarah Brodsky (TU Berlin)

Moduli of Tropical Plane Curves

\textit{Tropical curves} have been studied under two perspectives; the first perspective defines a tropical curve in terms of the \textit{tropical semifield} $\mathbb{T}=(\mathbb{R}\cup \{-\infty\}, \max, +)$, and the second perspective defines a tropical curve as a metric graph with a particular weight function on its vertices. Joint work with Michael Joswig, Ralph Morrison, and Bernd Sturmfels, we study which metric graphs of genus $g$ can be realized as smooth, plane tropical curves of genus $g$ with the motivation of understanding where these two perspectives meet.

Using \textit{Polymake}, \textit{TOPCOM}, and other computational tools, we conduct our study by constructing a map taking smooth, plane tropical curves of genus $g$ into the moduli space of metric graphs of genus $g$ and studying the image of this map. In particular, we focus on the cases when $g=2,3,4,5$. In this talk, we will introduce tropical geometry, discuss the motivation for this study, our methodology, and our results.

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