PIRSA:16040079 Conference Mathematical physics

DOI10.48660/16040079

Conference/School: Deformation Quantization of Shifted Poisson Structures

Brav, C. (2016). Relative non-commutative Calabi-Yau structures and shifted Lagrangians. Perimeter Institute. https://pirsa.org/16040079

Brav, Christopher. Relative non-commutative Calabi-Yau structures and shifted Lagrangians. Perimeter Institute, Apr. 20, 2016, https://pirsa.org/16040079 

@misc{ pirsa_PIRSA:16040079,
  doi = {10.48660/16040079},
  url = {https://pirsa.org/16040079},
  author = {Brav, Christopher},
  keywords = {Mathematical physics},
  language = {en},
  title = {Relative non-commutative Calabi-Yau structures and shifted Lagrangians},
  publisher = {Perimeter Institute},
  year = {2016},
  month = {apr},
  note = {PIRSA:16040079 see, \url{https://pirsa.org}}
}

Abstract

We give a definition of relative Calabi-Yau structure on a dg functor f: A --> B, discussing a examples coming from algebraic geometry, homotopy theory, and representation theory. When A=0, this returns the usual definition of Calabi-Yau structure on a smooth dg category B. When A itself is endowed with a Calabi-Yau structure and relative Calabi-Yau structure on f is compatible with the absolute structure on A, then we sketch the construction of a shifted symplectic structure on the derived moduli space M_A of pseudo-perfect A-modules, as well as the construction of a Lagrangian structure on the induced map f* : M_B --> M_A of derived moduli. This is joint work with Tobias Dyckerhoff.

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