# Relative orientations and the cyclic Deligne conjecture

### APA

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

### MLA

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

### BibTex

@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}} }

Nick Rozenblyum University of Chicago

## 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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