PIRSA:23100070 Scientific Series Mathematical physics

DOI10.48660/23100070

Series: Mathematical Physics

Rozenblyum, N. (2023). Relative orientations and the cyclic Deligne conjecture. Perimeter Institute. https://pirsa.org/23100070

Rozenblyum, Nikita. Relative orientations and the cyclic Deligne conjecture. Perimeter Institute, Oct. 03, 2023, https://pirsa.org/23100070 

@misc{ pirsa_PIRSA:23100070,
  doi = {10.48660/23100070},
  url = {https://pirsa.org/23100070},
  author = {Rozenblyum, Nikita},
  keywords = {Mathematical physics},
  language = {en},
  title = {Relative orientations and the cyclic Deligne conjecture},
  publisher = {Perimeter Institute},
  year = {2023},
  month = {oct},
  note = {PIRSA:23100070 see, \url{https://pirsa.org}}
}

Abstract

A consequence of the works of Costello and Lurie is that the Hochschild chain complex of a Calabi-Yau category admit the structure of a framed E_2 algebra (the genus zero operations). I will describe a new algebraic point of view on these operations which admits generalizations to the setting of relative Calabi-Yau structures, which do not seem to fit into the framework of TQFTs. In particular, we obtain a generalization of string topology to manifolds with boundary, as well as interesting operations on Hochschild homology of Fano varieties. Time permitting, I will explain some applications to quiver varieties. This is joint work with Christopher Brav.

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Zoom link: https://pitp.zoom.us/j/97363589637?pwd=T25YS0ZYQlBSWm5maXhQTklpSm50UT09

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