In this talk, we will discuss the construction of pseudodifferential operators on filtered manifolds and the semiclassical approach of partial differential equations (PDEs) that it allows. Indeed, a natural example of filtrations of the tangent space of a manifold is the one generated by the set of vector fields involved in the hypoellipticity of an operator via the Hörmander condition. Thus, there is a tight link between filtered manifolds and these operators, and it is not surprising that a pseudodifferential calculus adapted with the filtration is adequate for studying PDEs involving this operator. We will carefully define the items involved in the construction, and develop examples.
