BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Ivan Sechin (Skoltech) DTSTART:20210504T090000Z DTEND:20210504T092500Z DTSTAMP:20260423T023939Z UID:JGPW2021/8 DESCRIPTION:Title: Quantum R-matrix identities and Interacting Integrable Tops\nby Ivan Sechin (Skoltech) as part of Junior Global Poisson Workshop II\n\n\nAbstra ct\nIntegrability of classical integrable systems\, for example\, multi-pa rticle Calogero–Moser system\, is based on some functional identities on rational\, trigonometric\, or elliptic functions\, which ensure the exist ence of Lax pair and the Poisson commutativity of integrals of motion. It appears that some quantum R-matrices satisfy the matrix analogues of the r elations\, known as associative Yang–Baxter equation and its degeneratio ns. This fact allows us to use such quantum R-matrices in Lax pairs instea d of scalar functions and construct new classical integrable systems.\n\nI will describe the example of the application of quantum R-matrices relati ons in classical integrability\, introducing the system of interacting int egrable tops\, generalizing both Calogero–Moser systems of particles and Euler tops. I will also show how the resulting integrable structures simu ltaneously contain the properties of particle and top systems. If time per mits\, I briefly discuss the quantization of these structures\, in the ell iptic case it leads to quadratic quantum algebras which generalize both Sk lyanin algebra and Felder elliptic quantum group.\n LOCATION:https://researchseminars.org/talk/JGPW2021/8/ END:VEVENT END:VCALENDAR