 Tropical Geometry is the algebraic geometry over the min-plus algebra. It is a young subject that in recent years has both established itself as an area of its own right and unveiled its deep connections to numerous branches of pure and applied mathematics. From an algebraic geometric point of view, algebraic varieties over a field with non-archimedean valuation are replaced by polyhedral complexes, thereby retaining much of the information about the original varieties. From the point of view of complex geometry, the geometric combinatorial structure of tropical varieties is a maximal degeneration of a complex structure on a manifold.
The tropical transition from objects of algebraic geometry to the polyhedral realm is an extension of the classical theory of toric varieties. It opens problems on algebraic varieties to a completely new set of techniques, and has already led to remarkable results in Enumerative Algebraic Geometry, Dynamical Systems and Computational Algebra, among other fields, and to applications in Algebraic Statistics and Statistical Physics.
The goal of this program is, through its workshops and various other activities, to bring together researchers from the broad range of research areas involved, and to provide an extended forum of interaction on Tropical Geometry while it is still in its forming phase.
*Illustration from Jürgen Richter-Gebert, Bernd Sturmfels und Thorsten Theobald: First Steps in Tropical Geometry; in: Idempotent mathematics and mathematical physics, Contemp. Math., 377, AMS2005, pp. 289–317. |
