School of Mathematical Sciences

Moduli of Tropical Plane Curves menu

Moduli of Tropical Plane Curves

Speaker: 
Sarah Brodsky (TU Berlin)
Date/Time: 
Mon, 26/01/2015 - 16:30
Room: 
103
Seminar series: 

Tropical curves have been studied under two perspectives; the first perspective defines a tropical curve in terms of the tropical semifield T=(R∪{-∞}, 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 Polymake, 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.