  This is a report on recent progress concerning the interactions between
derived algebraic geometry and deformation quantization. We present the notion
of derived algebraic stacks, of shifted symplectic and Poisson structures, as
well as the construction of deformation quantization of shifted Poisson
structures. As an application we propose a general construction of the
quantization of the moduli space of $G$-bundles on an oriented space of
arbitrary dimension.
