November 26: Sylvain Carpentier

Title: The role of PreHamiltonian differential and difference operators in (classical) integrable systems.

Abstract:

We discuss a relatively new algebraic structure in the theory of integrable systems (of PDEs and differential-difference equations): the class of differential, or difference, operators such that their image is a sub Lie algebra of the algebra of evolutionary vector fields. These operators, called PreHamiltonian, encode most attributes of integrability for a given system. We will explain how they provide a natural non skew-symmetric generalization of the Hamiltonian (local and non-local) formalism, and discuss what is their geometric nature.