Amoebas of complex varieties and tropical algebraic geometry
speaker: Grigory Mikhalkin (University of Utah)abstract: This will be an introductory minicourse. Amoebas are images of algebraic varieties under the moment map $Log:({\mathbb C})n \to{\mathbb R}n$. They are closed unnbounded regions of peculiar shape which carry information on the initial algebraic variety. There exists a deformation (known in different areas of mathematics by different names: patchworking, dequantization, passing to the large complex limit) which turns the amoebas into piecewise-linear polyhedral complexes. It turns out that the resulting objects can be considered as algebraic varieties over the so-called tropical (or (max,+)) semiring. We'll also consider some applications of tropical geometry, such as computing the Gromov-Witten invariants of the projective plane (and other toric surfaces) by lattice paths in polygons.
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