Speaker
Prof.
Simonetta Abenda
(University of Bologna)
Description
We establish connections between two objects, naturally arising in the theory of the Kadomtsev-Petviashvily equation: totally nonnegative Grassmannians and rational degenerations of the M-curves (Riemann surfaces with an antiholomorphic involution and the maximal possible number of real ovals) with a collection of marked points.
More precisely, we show that a KP divisor satisfying the reality conditions on a degenerate M-curve is canonically associated to any point in the totally non--negative Grassmannian.
In the case of a certain rational degeneration of hyperelliptic M-curves, we also solve the inverse problem and explain the connection to the finite Toda system.
Primary author
Prof.
Simonetta Abenda
(University of Bologna)
Co-author
Prof.
Petr Grinevich
(Landau Institute)
