Jarmo Hietarinta – Thursday 12 March 2026

Speaker: Jarmo Hietarinta (University of Turku)

Title: Integrability and the decomposition of three-body interaction into pair-wise interactions

Abstract:

For a rather large class of integrable systems the dynamics can be described in terms of two-body interactions, such as scattering of particles or solitons. Furthermore, the interaction of three objects can be decomposed into (or built up from) a sequence of two-body interactions. In that situation the systems turns out to be integrable if and only if the final three-body result does not depend on which order the component two-body interactions take place. The canonical example is the collision of quantum particles on a line, leading to the Yang-Baxter equation. This has a natural extension to the set theoretical case, as exemplified by Yang-Baxter maps. But the same principle has still wider applications, and we will show how this paradigm can also be seen in the "Consistency-Around-a-Cube" concept for quad equations on a Z² lattice, and in the three-soliton condition of Hirota's bilinear formalism.