Title: Tropical curves, toric stacks, and enumerative geometry.

Abstract: In 2005 Mikhalkin found an elegant solution to the enumerative
problem of counting curves of a given genus on a toric surface. He used
symplectic methods to reduce the problem to enumeration of combinatorial
objects, called tropical curves, with certain multiplicities. Tropical
count was extended to the case of rational curves in higher dimensions
by Siebert and Nishinou using the techniques of log-geometry.

In this talk we will present an algebra-geometric point of view on
tropical curves. We will use tropical curves and toric stacks to assign
certain stacky limits to algebraic curves, and will discuss the problem
of reconstruction of the curve from its stacky limit. In particular we will
get another proof of the results of Mikhalkin, and Siebert-Nishinou.