The investigator and his colleagues are going to study operations on deformation complexes of various algebraic structures: in particular, operations on Hochschild cochains and chains of an associative algebra, and the deformation complex of d-algebras.
The knowledge of operations on Hochschild (co) chains should be useful for Index theory on a (degenerate) Poisson manifold, which is of great importance for Poisson geometry. Also, the investigator is trying to find a general simple construction of an operad acting on a deformation complex of a general algebraic structure. This can be helpful in studying deformations of such objects as Hopf algebras.
