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. 

https://indico.math.cnrs.fr/event/8941/