Derived bracket approach to $L_\infty$ algebras governing simultaneous deformations

In this talk we will present a way to explicitly construct $L_\infty$ algebras governing deformation problems for which several structures are simultaneously deformed. The typical examples include simultaneous deformations of two algebras and a morphism between them, or, in a geometrical context, of Poisson manifolds and their coisotropic submanifolds. This is a joint work with Marco Zambon (Madrid), and is based on a derived brackets construction due to T. Voronov.