Totally non-negative Grassmannians and rational 𝙼-curves in the KP-2 theory

For physical applications of the Kadomtsev-Petviashvili 2 equation it is necessary to know how to select real regular solutions. Multiline soliton solutions can be constructed using either Darboux-type transformations or by degenerating the finite-gap one. If the Darboux-type construction is applied, the real regular solutions correspond to points of totally non-negative Grassmannians. In the finite-gap approach real regular solutions correspond to 𝙼-curves (Riemann surfaces with maximal number of real ovals). The aim of our talk is to establish a bridge between these two important constructions. All necessary definitions will be presented during the talk. The talk is based on joint works with S. Abenda.