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

• 主讲人：Petr Grinevich (Steklov Mathematical Institute of RAS)
• 举办方： Beijing-Moscow Mathematics Colloquium
• 时间： 2024-06-07 17:00 - 2024-06-07 18:00
• 地点： Online

 

Recording: https://disk.pku.edu.cn/link/AA147E9BC1751D4652BB432128203991B7

 

Abstract: 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.

 

Bio: Petr Grinevich graduated from Moscow State University, Department of Mechanics and Mathematics in 1981, received PhD in 1984, scientific advisor Sergei Novikov, received doctor degree in 1999. Starting 1999 he worked in L.D. Landau Institute for Theoretical Physics RAS, starting 2019 he works in Steklov Mathematical Institute, RAS. His research interests lie in mathematical physics, including integrable equations and scattering theory.