AKSZ quantization of shifted Poisson structures
APA
Rozenblyum, N. (2016). AKSZ quantization of shifted Poisson structures. Perimeter Institute. https://pirsa.org/16040085
MLA
Rozenblyum, Nikita. AKSZ quantization of shifted Poisson structures. Perimeter Institute, Apr. 22, 2016, https://pirsa.org/16040085
BibTex
@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}} }
University of Chicago
Talk Type
Subject
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.