Program

Tropical geometry can be viewed as a degenerate version of algebraic geometry,where the role of algebraic varieties is played by certain polyhedral complexes. As the degeneration process, called tropicalization, preserves many fundamental properties, tropical geometry provides important bridges and an exchange of methods between algebraic geometry, symplectic geometry and convex geometry; these links have been extremely fruitful and gave rise to remarkable results during the last 20 years. The main focus of the program will be on the most significant recent developments in tropical geometry and its applications. The following topics are particularly influential in the area and will be central in the program: real aspects of tropical geometry; tropical mirror symmetry and non-Archimedean geometry; tropical phenomena in symplectic geometry; matroids, combinatorial and algebraic aspects; tropical moduli spaces; tropical geometry and A1-homotopy theory.