Topological duality for formal Whitney and polynomial tempered growth functors

(joint work with Ana Rita Martins, Univ. Católica) We shall review on classic results on the topological dualiy between distributions with compact support and C^{\infty} functions on a subanalytic set. Next we review the Whitney and moderate growth functors introduced by Kashiwara and Schapira in the 90ties and their results on the natural topological duality between them. We shall explain the new framework of modules over the sheaf of formal differential operators in a parameter \hbar in connexion with deformation quantization. Finally we shall explain how to extend the natural topological duality to this new setting and treat simple examples.