Moscow--Petersburg seminar on low-dimensional mathematics SPb, PDMI, 04.10.2002, 16:00--17:45, room 311 "Gromov-Witten invariants and lattice paths in polygons" G.Mikhalkin (PMDI--Utah) The talk presents a new formula for the Gromov-Witten invariants of arbitrary genus in the projective plane, the product of two lines and other toric surfaces. It turns out that such invariants can be computed as a number (counted with multiplicities) of certain lattice paths connecting two vertices of the relevant Newton polygon. Seminar home-page http://www.pdmi.ras.ru/~lowdimma