Dimitri Zvonkine | The KdV hierarchy: a system of PDEs from an algebraist’s point of view 3/4
Channel: EIMI, PDMI RAS and Chebyshev Laboratory
Date: 2021-11-23

School "Moduli Spaces, Combinatorics and Integrable Systems", November 22, 2021
Dimitri Zvonkine (Université de Versailles Saint-Quentin-en-Yvelines)
The Korteweg – de Vries hierarchy: a system of PDEs from an algebraist’s point of view (3/4)

We will describe three approaches to the KdV hierarchy.
The definition via pseudo-differential operators and Lax pairs allows one to construct the equations of the hierarchy and prove some of their properties.
The approach via the infinite-dimensional Sato Grassmannian makes it possible to construct solutions of the hierarchy without even looking at the equations.
Finally, the most recent approach via the intersection theory on moduli spaces of curves, allows one to construct the hierarchy, its ”quantum” version, and generalizes to many other integrable hierarchies.