Matteo Casati: Poisson cohomology for difference systems

Salle 318 (IMB)

Salle 318 (IMB)


Integrable differential-difference systems are endowed with biHamiltonian structures defined by difference operators, contrasting with the better known case of Hamiltonian PDEs. I will present a geometric framework for the investigation of such Hamiltonian operators, in particular defining and computing the cohomology of the corresponding functional bivectors. I will present the results obtained together with J.P. Wang in [Commun. Math. Phys. 2019], together with some new results in the multi-component case.