Mathematics

The course is centered on the Hamiltonian aspects of integrable systems of Ordinary and Partial Differential Equations, with a focus on the geometrical side. After having reviewed the relevant notions of symplectic and Poisson geometry the following issues will be discussed

i) Group actions on Poisson manifolds and the Marsden-Weinstein reduction theorem.

ii) Distributions and the Marsden-Ratiu and Dirac reduction schemes.

iii) Lie-Poisson structures on duals of Lie algebras.

iv) Bihamiltonian structures

v) Drinfel’d-Sokolov reduction on loop algebras and equations of KdV type.ac reduction schemes.