Theodore Voronov (University of Manchester)
I will recall how a Poisson structure on a manifold is defined in terms on derived brackets and how the Koszul bracket on differential forms arises for a Poisson manifold. Then I will discuss a generalization of Koszul brackets to the case of "higher" or "homotopy" Poisson structure. The aim is to introduce to the ideas of our paper http://arxiv.org/abs/0808.3406. (There is an interesting open question there.) This is meant to be a mild introduction to various structures arising on the way.