Serdecznie zapraszamy na seminarium "Geometria i Układy Dynamiczne". Seminarium odbędzie się 20.07.2023 (czwartek), w godzinach 13:15-15:00 w sali A1/22.
Prelegent: Pavlos Kassotakis (Wydział Fizyki, Uniwersytet Warszawski)
Title: Matrix factorizations, Yang-Baxter and pentagon maps
Set-theoretical solutions of the Pentagon relation, also referred to as pentagon maps, turn to be essentially three-dimensional discrete integrable systems. In this talk we focus into a connection of the pentagon maps with discrete integrability, via Lax pair formulation. In detail, we propose a specific class of matrices that participate to factorization problems that turn to be equivalent to constant and entwining (non-constant) pentagon maps, expressed in totally non-commutative variables. We show that factorizations of order N = 2 matrices of this specific class, turn equivalent to the homogeneous normalization map, while from order N = 3 matrices we obtain an extension of the homogeneous normalization map, as well as novel entwining pentagon, reverse-pentagon and Yang-Baxter maps.
A. Denisiuk, A. Doliwa, V. Shevchishin, A. Siemaszko