Tropical KP theory

Date

Mar 26, 2026

Time

3:00 PM - 4:00 PM

Speaker

Yelena Mandelshtam

Affiliation

University of Michigan

Language

en

Main Topic

Biologie

Host

Local Organisers: Nikola Sadovek, Maximilian Wiesmann, Giulio Zucal

Description

The Kadomtsev–Petviashvili (KP) equation is a central example of an integrable nonlinear PDE with deep connections to algebraic geometry. A classical construction of Krichever produces quasi-periodic solutions from algebraic curves together with divisor data via Riemann theta functions. At the same time, soliton solutions have a rich combinatorial structure: work of Kodama-Williams and others relates them to the geometry and combinatorics of the positive Grassmannian. In this talk I will describe recent and ongoing work with several collaborators that develops a “tropical KP theory’’ connecting these two viewpoints. When an algebraic curve degenerates to a tropical curve, the associated theta-function solutions collapse to soliton solutions. We show that the algebro-geometric data in the Krichever construction admits a direct tropical/combinatorial description that determines the resulting soliton solution. In particular, one can translate the geometric data of the degeneration into purely combinatorial objects that encode the soliton structure. This perspective provides a concrete way to pass from algebraic curves to soliton solutions and reveals a new combinatorial layer underlying the classical algebro-geometric theory of KP.

Last modified: Mar 14, 2026, 7:39:47 AM