Quantization of contact and symplectic complex manifolds

In 1992, M. Kashiwara has constructed the stack of modules of microdifferential operators on a complex contact manifold and recently I. Waschkies has constructed the stack of microlocal perverse sheaves. In this talk, we shall recall these constructions and explain how to treat the symplectic case by adding a central parameter, similarly as in quantization deformation theory.