Real algebraic varieties close to smooth tropical limits

This talk is based on joint work with Kris Shaw and Arthur Renaudineau. 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. We have two motivations in mind: Firstly, in generalisation of Viro's combinatorial patchwoking to arbitrary codimension, the arising PL-geometries 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.