# Jerusalem Mathematics Colloquium

Thursday, 6th November 2003, 4:00 pm

Mathematics Building, Lecture Hall 2

##

Professor Evgenii Shustin

(Tel Aviv)

"Tropical and classical algebraic geometry"

** Abstract: ** The tropical algebraic geometry, i.e. algebraic geometry over
tropical (idempotent) semi-rings, has recently found fascinating
applications to the enumeration of complex and real algebraic curves,
and computing Gromov-Witten invariants of toric surfaces.

The idea of the tropical approach to these enumerative problems
(Kontsevich, Mikhalkin) consists in reducing the count of algebraic
curves to the count of tropical curves (non-Archimedean amoebas),
which are just planar graphs dual to lattice subdivisions of
Newton polygons.

We give an explanation of the link between the tropical and classical
geometry, based on the presentation of a tropical object as limit
(dequantization) of a classical object, and vice versa, a classical
object as deformation (quantization) of a tropical object.

We shall discuss an application of the tropical approach to enumeration
of real rational curves and computation of the Welschinger invariant
(the Gromov-Witten invariant over the reals).

Light refreshments will be served in the faculty lounge at 3:30.

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