Derived Algebraic Geometry and Deformation Quantization

Understand

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.