|Location:||MSRI: Baker Board Room|
Purely real Welschinger invariants of real Del Pezzo surfaces count real rational curves in a given linear system which match suitable number of real generic points and are equipped with weights \pm 1. Tropical geometry provides a powerful tool to study Welschinger invariants and leads to a series of results, among them recursiv formulas of Caporaso-Harris type, the positivity of all purely real Welschinger invariants and their logarithmic asymptotic equivalence to the genus zero Gromov-Witten invariants, which by now are proved for real Del Pezzo surfaces with K2>3. An important by-product of the tropical approach is the discovery of tropical Welschinger invariants which are defined for any genus and arbitrary toric surfaces and might correspond to still unknown algebraic invariants.
Joint work with I. Itenberg and V. Kharlamov.