## Thick morhisms and higher Koszul brackets

#### Dr Hovhannes Khudaverdian (University of Manchester)

In the talk, we shall present a homotopy analog of the above results.  When an ordinary Poisson structure is replaced by a homotopy one, instead of a single Koszul bracket there arises an infinite sequence of "higher Koszul brackets" introducing an $L_{\infty}$-algebra structure in the space of differential forms.  (See Khudaverdian-Voronov, 2008, http://arxiv.org/abs/0808.3406.)  We shall show how to use thick morphisms of supermanifolds to construct a non-linear transformation, which is an $L_{\infty}$-morphism, from this $L_{\infty}$-algebra of differential forms to the Lie superalgebra of multivector fields with the canonical Schouten bracket.