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.