Cotangent complexes of moduli spaces and Ginzburg dg algebras

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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