Amoebas and tropical geometry

October 23 to 26, 2003

at the

American Institute of Mathematics, Palo Alto, California

organized by

Grigory Mikhalkin, Bernd Sturmfels, and Oleg Viro

This workshop, sponsored by AIM and the NSF, will be devoted to a brand-new subject which we call tropical geometry. Tropical varieties are piecewise-linear objects in Euclidean space. The link between the classical complex geometry and the tropical geometry is provided by amoebas or logarithmic images of complex varieties. The tropical varieties appear as certain degenerations of amoebas. This workshop will bring together researchers in such diverse areas as real algebraic geometry, mirror symmetry, control theory, mathematical physics, analysis of several variables and dynamics. Amoebas, tropical geometry and the degeneration which relates them appeared in some form in all of these areas. We hope especially to set foundations of the new subejct and explore its applications.

The main topics for the workshop are

Tropical vs. classical algebraic geometry. Connections to physics.
Amoebas in symplectic geometry. Lagrangian torus bundles.
Links to probability theory and dynamical systems.
Patchworking in real algebraic geometry.

This workshop is a lead-in to the MSRI program Topological Aspects of Real Algebraic Geometry. Particular attention will be devoted to preparing recent PhDs who will be participating in the MSRI program.

The workshop will differ from typical conferences in some regards. Participants will be invited to suggest open problems and questions before the workshop begins, and these will be posted on the workshop website. These include specific problems on which there is hope of making some progress during the workshop, as well as more ambitious problems which may influence the future activity of the field. Lectures at the workshop will be focused on familiarizing the participants with the background material leading up to specific problems, and there will be ample time between talks for discussions and for work to be done.

Invited participants include V. Batyrev, A. Bertram, B. Bertrand, A. Cannas da Silva, A. Grassi, M. Gross, E. Ionel, I. Itenberg, M. Kapranov, M. Kontsevich, S. Kwon, D. Lind, G. Litvinov, A. Losev, D. Maclagan, G. Mikhalkin, D. Novikov, Y.-G. Oh, A. Okounkov, M. Passare, T. Sadykov, F. Sottile, B. Sturmfels, M. Symington, T. Theobald, G. Tian, O. Viro, J.-Y. Welschinger, and S. Zelditch.

The application deadline to participate in this workshop has passed.

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