Counting Plane Tropical Curves via Lattice Paths in Polygons

The number of projective plane tropical curves, counting multiplicity, of degree d and genus g passing through n = 3d + g -1 points in general position in the plane does not depend on the individual points, other than that they be in general position. This number of curves is called a tropical Gromov-Witten invariant and agrees with the Gromov-Wittten invariants in algebraic geometry. I will discuss the proof of a theorem of Mikhalkin that allows one to compute the Gromov-Written invariant by a purely combinatorial process of counting certain lattice paths.