Tondo G. Beyond recursion operators: Haantjes algebras (abstract)
Speaker: Giorgio Tondo
Title: Beyond recursion operators: Haantjes algebras
I will illustrate in detail the notion of Haantjes algebra, recently introduced to generalize the very successful Magri's theory of recursion operators for soliton equations. Haantjes algebras are associative and commutative algebras of operators with vanishing Haantjes torsion, over differentiable manifolds. In such a context, the powers of a recursion operator are replaced by a distinguished basis of a Haantjes algebra. The case of semisimple Haantjes algebras over symplectic manifolds, leading to separation of variables for Hamilton-Jacobi equations associated with separable Hamiltonian systems, will be analyzed. Also, some examples of non semisimple Haantjes algebras coming from the theory of hydrodynamic-type systems, will be presented.
Event: Local and Nonlocal Geometry of PDEs and Integrability, 8-12 October 2018, SISSA, Trieste, Italy.
The conference in honor of Joseph Krasil'shchik's 70th birthday.