# Cotangent complexes of moduli spaces and Ginzburg dg algebras

### APA

Scherotzke, S. (2020). Cotangent complexes of moduli spaces and Ginzburg dg algebras. Perimeter Institute. https://pirsa.org/20060025

### MLA

Scherotzke, Sarah. Cotangent complexes of moduli spaces and Ginzburg dg algebras. Perimeter Institute, Jun. 23, 2020, https://pirsa.org/20060025

### BibTex

@misc{ pirsa_PIRSA:20060025, doi = {10.48660/20060025}, url = {https://pirsa.org/20060025}, author = {Scherotzke, Sarah}, keywords = {Mathematical physics}, language = {en}, title = {Cotangent complexes of moduli spaces and Ginzburg dg algebras}, publisher = {Perimeter Institute}, year = {2020}, month = {jun}, note = {PIRSA:20060025 see, \url{https://pirsa.org}} }

University of Luxembourg

**Collection**

Talk Type

**Subject**

Abstract

We give an introduction to the notion of moduli stack of a dg category.
We explain what shifted symplectic structures are and how they are
connected to Calabi-Yau structures on dg categories. More concretely,
we will show that the cotangent complex to the moduli stack of a dg
category A admits a modular interpretation: namely, it is isomorphic
to the moduli stack of the *Calabi-Yau completion* of A. This answers
a conjecture of Keller-Yeung. The talk is based on joint work
This is joint work with Damien Calaque and Tristan Bozec
arxiv.org/abs/2006.01069