Event

Set-theoretic Yang-Baxter equation and related integrable maps

  • Thu 5 Dec 19

    14:00 - 16:00

  • Colchester Campus

    STEM Centre 3.1

  • Event speaker

    Dr George Papamikos

  • Event type

    Lectures, talks and seminars
    Mathematical Sciences Departmental Seminars

  • Event organiser

    Mathematical Sciences, Department of

  • Contact details

    Andrew Harrison

Mathematical Sciences Departmental Seminar

These Departmental Seminars are for everyone interested in Maths. We encourage anyone interested in the subject in general, or in the particular subject of the seminar, to come along. It's a great opportunity to meet people in the Maths Department and join in with our community. 

Refreshments are shared in the Department (STEM 5.1) after every seminar.

Set-theoretic Yang-Baxter equation and related integrable maps

Dr George Papamikos

We study some solutions of the set-theoretic parametric Yang-Baxter equation. These solutions are bi-rational maps with several invariants and a Lax representation [1]. We show that we can use these maps as building blocks in order to construct higher dimensional bi-rational maps which have nice properties and we prove their integrability in the Liouville sense. These maps can be seen as higher dimensional generalisations of the famous integrable QRT maps [2], known as Adler's Triad maps [3]. Finally, we discuss some new generalisations [4].

References

[1] A. P. Veselov, Yang-Baxter maps and integrable dynamics, Physics Letters A 314 (2003), 214 - 221. 
[2] G. R. W. Quispel, J. A. G. Roberts, C. J. Thompson, Integrable mappings and soliton equaions II, Physica D: Nonlinear Phenomena 34 (1989), 183-192.
[3] S. Konstantinou-Rizos, G.Papamikos, Entwining Yang-Baxter maps related to NLS type equations, arXiv:1907.00019
[4] V. E. Adler, On a class of third order mappings with two rational invariants, preprint, arXiv:nlin/0606056v1.

Speaker

Dr George Papamikos is a Research Fellow in the School of Mathematics, University of Leeds.