TGiZ-Seminar: Tropical geometry in Zoom (Second meeting)

Johannes Rau (Universidad de los Andes)

Abstract:
I will present a combinatorial setup, based on smooth tropical varieties and real phase structures, which after “unfolding” produces a certain class of PL-manifolds (called patchworks). We have two motivations in mind: Firstly, in the spirit of Viro’s combinatorial patchwoking for hypersurfaces, these patchworks can be used to describe the topology of real algebraic varieties close to the tropical limit. Secondly, even if not “realisable” by real algebraic varieties, real phase structures provide a geometric framework for combinatorial structures such as oriented matroids. Joint work with Arthur Renaudineau and Kris Shaw.