KP equations, M curves and nonnegative Grassmannians, Piotr Grinevich

Title: KP equations, Mcurves and nonnegative Grassmannians Abstract: In the theory of KP2 equations there exist two methods to determine real nonsingular multisoliton solutions (whose geometrical properties are quite intriguing and closely related to Tropical Geometry). The first method is by doing Darboux transformations in the points of a completely nonnegative Grassmannians. The second method is by degenerating Mcurves with properly chosen divisors. Both objects nonnegative Grassmanians and Mcurves) show up in many different problems in various branches of Mathematics. The purpose of our work was to investigate the way in which these two objects are related with each other. In more formal terms, to find a method to associate a degenerate Mcurve with a divisor on it to a point in nonnecgative Grassmannian, so that the corresponding KP2solutions are the same. Based on joint papers with S. Abenda