PIRSA:16040085 Conference Mathematical physics

DOI10.48660/16040085

Conference/School: Deformation Quantization of Shifted Poisson Structures

Rozenblyum, N. (2016). AKSZ quantization of shifted Poisson structures. Perimeter Institute. https://pirsa.org/16040085

Rozenblyum, Nikita. AKSZ quantization of shifted Poisson structures. Perimeter Institute, Apr. 22, 2016, https://pirsa.org/16040085 

@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.

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