Speaker: Sotiris Konstantinou-Rizos (P.G. Demidov Yaroslavl State University, Russia)
Date and time: 15.03.2023, 17:00 (GMT +03:00)

Title: Correspondences and N-simplex maps on groups and rings

The Yang--Baxter equation and Zamolodchikov's tetrahedron equation are two of the most fundamental equations of Mathematical Physics, and they are members of the general family of n-simplex equations for n=2 and n=3, respectively. The study of n-simplex maps, namely set-theoretical solutions to the n-simplex equation, was formally initiated by Drinfeld for n = 2.

In this talk, I will present new methods for constructing new solutions to 3- and 4-simplex equations. I will demonstrate the role of correspondences for deriving new n-simplex maps which do not belong to any of the known classification lists. Next, I will present some new tetrahedron maps on groups and rings. Moreover, I will show a method for constructing nontrivial 4-simplex extensions of tetrahedron maps. Finally, I will present some new n-simplex maps.

This talk is mainly based on the following papers:

[1] S. Konstantinou-Rizos, "Birational solutions to the set-theoretical 4-simplex equation," to appear in Physica D: Nonl. Phen. (2023).
[2] S. Igonin, S. Konstantinou-Rizos,  "Set-theoretical solutions to the Zamolodchikov tetrahedron equation on groups and their Lax representations," arXiv:2302.03059 (2023)
[3] S. Konstantinou-Rizos, Noncommutative solutions to Zamolodchikov’s tetrahedron equation and matrix six-factorisation problems, Physica D: Nonl. Phen. 440 (2022), 133466.

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