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
Links:
[1] http://www.mpim-bonn.mpg.de/taxonomy/term/39
[2] http://www.mpim-bonn.mpg.de/grt2020