Brian Mann
Tropical Curves
A tropical curve is, loosely, a balanced graph in the real plane which
can be gotten as some sort of degeneration of the image of a complex
algebraic curve under some map. I will briefly discuss the motivation
for studying tropical curves (how they arise from algebraic objects, and
how properties of tropical curves relate to properties of algebraic
curves), and then concentrate solely on the combinatorial properties of
such objects. Namely, I will talk about the problem of enumerative
geometry, and a combinatorial criterion to tell when a tropical curve is
irreducible.