Eugene Ferapontov (Loughborough University)
E.V.Ferapontov@lboro.ac.uk
Many important equations of mathematical physics possess Hamiltonian formulation. The corresponding Poisson brackets (Hamiltonian operators) are interesting objects in their own and have interesting connections with algebra and differential geometry. Although the general problem of the classification of all Hamiltonian operators is far from a complete solution (it can't even be formulated precisely), there exist various partial classification results. In this talk we will be mainly concerned with a special class of Poisson brackets of differential-geometric type, typical for one-dimensional hyperbolic quasilinear systems. It will be demonstrated that the classification of such brackets can be reformulated as a classical differential-geometric problem.