Speaker:  Anastasios Tongas (University of Patras, Greece)

Date and time: 28.10.2020, 17:00 (GMT +03:00)

Title: Tetrahedron maps and symmetries of three dimensional integrable discrete equations

Abstract:  The aim of this talk is to explain that the study of discrete integrable equations on $Z^3$ and their symmetry group of transformations is intimately connected with solutions of the functional tetrahedron (Zamolodchikov) equation, and vice versa.

First, I will review the two dimensional situation in connection with the famous Yang-Baxter equation, and then I will give a detailed analysis of this link in the three dimensional case and the tetrahedron equation.

I will also discuss the basic notions on the symmetry group of transformations of lattice equations,  with particular emphasis given on the dual formulation of Frobenius Theorem in terms of differential forms. The latter provides us an elegant way for constructing a complete set of G–invariants under a regular action.

As an application I will demonstrate the method by a case–by–case analysis of the octahedron type lattice equations classified recently, leading to some new examples of tetrahedron maps and integrable coupled lattice equations.

The talk is based on recent ongoing joint work with Pavlos Kassotakis, Maciej Nieszporski and Vassilis Papageorgiou.

To access the online seminar please contact  Anna Tolbey bekvaanna@gmail.com