2023 CIMPA School

Crossroads of geometry, representation theory and higher structures

Sarah Scherotzke (Université du Luxembourg) Cotangent complexes of moduli spaces and Ginzburg differential graded algebras. First, we give an introduction to the notion of moduli stack of a differential graded category. Then 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 differential graded category A is isomorphic to the moduli stack of the “Calabi–Yau completion” of A, answering a conjecture of Keller–Yeung. This is joint work with Damien Calaque and Tristan Bozec, see arxiv.org/abs/2006.01069.