### The Moduli Space of Weighted Stable Tropical Curves

By Martin Ulirsch

September 18, 2013

#### Abstract

We propose a definition of weighted stability for abstract tropical curves depending on an certain weights and construct a natural parameter space of these objects. We will discuss its structure and natural maps between such spaces induced by varying weights. In the end I am going to state a conjecture connecting this purely combinatorial theory to Hassett's moduli space of weighted stable algebraic curves.

**P.S.** The prerequisites for the first 40 minutes will be: graphs, metric spaces and finite group actions. Only the last 10 minutes will require some background in algebraic geometry.