BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Talks.cam//talks.cam.ac.uk//
X-WR-CALNAME:Talks.cam
BEGIN:VEVENT
SUMMARY:Lagrangian multiforms: a variational criterion for integrability -
  Vincent Caudrelier (University of Leeds)
DTSTART:20221021T140000Z
DTEND:20221021T143000Z
UID:TALK182618@talks.cam.ac.uk
DESCRIPTION:I will present the relatively recent notion of Lagrangian mult
 iforms whose aim is to capture integrability in a purely variational fashi
 on. Lagrangian multiforms are ubiquitous in classical integrable models: t
 hey can be defined and used in continuous or discrete systems\, finite or 
 infinite dimensional (field theories). So far\, the Hamiltonian formalism 
 has been the overwhelming winner to define integrability\, rooted in the L
 iouville-Arnold theorem. I will show how Lagrangian multiforms offer varia
 tional counterparts to the established Hamiltonian criteria for integrabil
 ity\, e.g. Poisson commuting Hamiltonians or the appearance of the classic
 al Yang-Baxter equation. This continues the long interplay between Hamilto
 nian and Lagrangian formalisms\, within the realm of integrability. Each o
 ne offers advantages and limitations. I will argue that\, for field theori
 es\, Lagrangian multiforms offer a covariant and more natural criterion fo
 r integrability than the Hamiltonian counterpart. As a main example\, I wi
 ll use the AKNS hierarchy which contains several famous equations\, e.g. n
 onlinear Schr&ouml\;dinger. I will comment on the open issue of quantizati
 on with hints that Feynman path integral techniques could perhaps be used.
  A long-term goal\, but at this stage speculative\, would be to offer a pa
 th integral alternative to the well-established\, Hamiltonian driven\, mac
 hinery of the Quantum Inverse Scattering Method.&nbsp\;
LOCATION:Seminar Room 1\, Newton Institute
END:VEVENT
END:VCALENDAR