VIRTUAL SEMINAR SERIES -- INTEGRABLE SYSTEMS: Nonabelian Hamiltonian (integrable) systems - double, lambda and Schouten brackets
Matteo Casati (University of Kent/Ningbo University)
Wednesday 23rd September, 2020 13:30-14:30 Zoom seminar hosted by ICMS
Poisson brackets are an essential tool in the description of Integrable Systems. They at the same time endow the space of "observables" with the structure of a Lie algebra (allowing us to identify the conserved quantities of the system) and describe the action of the observables on the phase space (providing us with the Hamiltonian equations). Integrable nonabelian systems of equations (namely, systems in which the field variables take values in a nonabelian algebra, as in matrix-valued systems) can be described by the same general structure, but the underlying Poisson algebra should be replaced by the so-called double Poisson algebra. This has been established by Van Den Bergh for systems of ODEs and, more recently, by De Sole, Kac and Valeri for systems of PDEs. In this talk I would like to enlarge the landscape including integrable differential-difference equations, and cast the algebraic picture of double Poisson (and quasi-Poisson) algebras in geometrical terms.
For more information, and how to access the seminar through Zoom, see the webpage of the events here.