Seminar 09.04.2025: Pavlos Kassotakis (University of Patras, Greece)

Title: On pentagon and entwining tetrahedron maps Abstract: In this talk, we present equivalence classes of rational solutions of a specific type of the set theoretical version of the pentagon equation. That is, up to Möbius transformations, we find quadrirational one-component maps of rational functions in two arguments that serve as solutions of the pentagon equation. Also, provided that a pentagon map admits at least one partial inverse, we obtain entwining pentagon set theoretical solutions. Furthermore, we show how to obtain Yang–Baxter and entwining tetrahedron maps from pentagon maps.