A tropical calculation of the Welschinger invariants of real toric Del Pezzo surfaces

The Welschinger invariants of real rational algebraic surfaces are natural analogues of the genus zero Gromov-Witten invariants. We establish a tropical formula to calculate the Welschinger invariants of real toric Del Pezzo surfaces for any conjugation-invariant configuration of points. The formula expresses the Welschinger invariants via the total multiplicity of certain tropical curves (non-Archimedean amoebas) passing through generic configurations of points, and then via the total multiplicity of some lattice paths in the convex lattice polygon associated with a given surface. We also present the results of computation of Welschinger invariants, obtained jointly with I. Itenberg and V. Kharlamov.