KTH/SU Mathematics Colloquium

May 17, 2006

Ilia Itenberg (Strasbourg)

"Tropical geometry and asymptotic enumeration of real rational curves"

ABSTRACT The goal of the talk is to give a brief introduction to tropical geometry and to present its applications in real enumerative geometry. The recent appearance of tropical geometry was motivated by its multiple and deep relations with different branches of mathematics. An important link between the complex world and the tropical one is given by Mikhalkin's correspondence theorem. This theorem together with the discovery of the Welschinger invariants (these invariants can be seen as a real analog of the Gromov-Witten invariants) give rise to several results concerning the enumeration of real rational curves on algebraic surfaces.