BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Vincent Caudrelier DTSTART:20260116T080000Z DTEND:20260116T090000Z DTSTAMP:20260423T010620Z UID:nmps/12 DESCRIPTION:Title: Cl assical Yang-Baxter equation\, Lagrangian multiforms and ultralocal integr able hierarchies\nby Vincent Caudrelier as part of Nagoya Math-Phys Se minar\n\n\nAbstract\nI will first review the main ideas of Lagrangian mult iform theory which provides a variational framework for integrable systems \, focusing on 1+1 dimensional models. The key idea is to encode variation ally the compatibility of the flows in an integrable hierarchy by introduc ing a generalisation of standard Lagrangians and action functionals\, and a corresponding generalisation of the principle of least action. \n\nI wil l then present a systematic construction of Lagrangian multiforms for hier archies of ultralocal field theories. The ''multitime'' Euler-Lagrange equ ations produce the infinite collection of flatness equations for the Lax c onnection. It is based on a few key (algebraic) ingredients\, the main one being the classical r-matrix and the classical Yang-Baxter equation. In p articular\, the construction casts the classical Yang-Baxter in a variatio nal context for the first time. For simplicity of exposition\, I will focu s on the simplest example of the so-called Ablowitz-Kaup-Newell-Segur hier archy which already contains all the essential features (classical r-matri x\, generating formalism). I will then explain briefly how these features generalise to produce Lagrangian multiforms for many other (known and new) hierarchies : e.g. Zakharov-Mikhailov\, Faddeev-Reshetikhin model\, defor med sigma/Gross-Neveu models. Time permitting\, I will explain how one can easily couple different hierarchies together to form new ones and obtain the corresponding Lagrangian multiform.\n LOCATION:https://researchseminars.org/talk/nmps/12/ END:VEVENT END:VCALENDAR