Speaker: Pavlos Kassotakis (University of Kent, UK; Centre of Integrable Systems, P.G. Demidov Yaroslavl State University, Russia)

Date and time: 27.04.2022, 17:00 (GMT +03:00)

Title: Hierarchies of compatible maps and integrable difference systems

Abstract: We introduce families of non-Abelian compatible maps associated with Nth order discrete spectral problems. In that respect we have hierarchies of families of compatible maps that in turn are associated with hierarchies of set-theoretical solutions of the 2-simplex equation a.k.a Yang-Baxter maps. These hierarchies are naturally associated with integrable difference systems with variables defined on edges of an elementary cell of the $\mathbb{Z}^2$ graph, that in turn lead to hierarchies of difference systems with variables defined on vertices of the same cell. Furthermore, these hierarchies with vertex variables are point equivalent with the explicit form of what will be called non-Abelian lattice-NQC(Nijhoff-Quispel-Capel) Gel'fand-Dikii hierarchy.

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