Real structures on tropical varieties

Abstract: We will propose a definition of a real structure on a non-singular projective tropical variety. This definition takes its inspiration from Viro's patchworking theorem. In the local setting, we will prove that such a structure on a matroidal fan is equivalent to an orientation on the underlying matroid. We will then generalize Viro's theorem to this setting. This is a joint work with Johannes Rau and Kris Shaw.