Since Schlessinger and Stasheff introduced the notion of homotopy Lie algebra, a lot of attention has been paid to this field by mathematicians and physicists due to its relation to a variety of topics. In this talk, we focus on the Poisson geometry aspect. We study Maurer-Cartan elements on homotopy Poisson manifolds. As a byproduct, we generalize the AKSZ formalism to the case of homotopy symplectic manifolds. Then we construct a Courant algebroid from a 2-term Linfty algebra. This construction is used to derive a new one from a given one, thus producing many interesting examples. By integrating the Lie quasi-bialgebroid associated to the Courant algebroid, we obtain a Lie-quasi-Poisson groupoid, which is proposed to be the geometric structure on the dual of a 2-term Linfty algebra.

This talk is based on a joint work with H. Lang and Y. Sheng.