Vertex algebra and Poisson vertex algebra cohomology

Professor Alberto de Sole, Universita' di Roma, La Sapienza.

We present an operadic approach to vertex algebra cohomology. A general construction associates a cohomology complex to a linear operad. In the case of the chiral operads we get a vertex algebra cohomology complex. Likewise, the associated graded of the chiral operad leads to a classical operad, which produces a Poisson vertex algebra cohomology complex. The latter is closely related to the variational Poisson cohomology.