# Manchester Geometry Seminar 2008/2009

**Thursday 2 October 2008. ** *The Frank Adams Room (Room 1.212), the Alan Turing Building. 4pm*
##
Differential Forms and Higher Poisson Brackets

Theodore Voronov (University of Manchester)

`theodore.voronov@manchester.ac.uk`

We show how the relation between Poisson brackets and symplectic forms can be extended to the case of inhomogeneous multivector fields and inhomogeneous differential forms (or pseudodifferential forms). In particular we arrive at a notion which is a generalization of a symplectic structure and gives rise to higher Poisson brackets. We also obtain a construction of Koszul type brackets in this setting.

The talk is based on a joint work of Hovhannes Khudaverdian and the speaker: arXiv:0808.3406v1 [math-ph].

Keywords: *Higher Poisson bracket, strongly homotopy Lie algebra, supermanifold, symplectic form, Legendre transformation, higher Koszul bracket*.