AKSZ quantization of shifted Poisson structures

          @misc{ pirsa_PIRSA:16040085,
            doi = {10.48660/16040085},
            url = {https://pirsa.org/16040085},
            author = {Rozenblyum, Nikita},
            keywords = {Mathematical physics},
            language = {en},
            title = {AKSZ quantization of shifted Poisson structures},
            publisher = {Perimeter Institute},
            year = {2016},
            month = {apr},
            note = {PIRSA:16040085 see, \url{https://pirsa.org}}
          }
          

Abstract

One of the key constructions in the PTVV theory of shifted symplectic structures is the construction, via transgression, of a shifted symplectic structure on the derived mapping stack from an oriented manifold to a shifted symplectic stack vastly generalizing the AKSZ construction (which was formulated in the context of super manifolds). I will explain local-to-global approach to this construction, which also generalizes the construction to shifted Poisson structures and shows that the AKSZ/PTVV construction is compatible with quantization in a strong sense. One pleasant consequence is that every deformation quantization problem reduces to a version of BV-quantization. Time permitting, I will describe several geometric applications of the theory.