An operadic proof of the Bogomolov–Tian–Todorov theorem

In this article, we explain an operadic proof of the Bogomolov-Tian-Todorov (BTT) theorem stating that the deformation theory of Calabi-Yau varieties is unobstructed. We also provide a short new proof of the non-commutative BTT for Calabi-Yau dg categories. Finally, we observe that our proof also produces partial results in positive characteristic. This article is part of the theme issue 'Derived Lie algebras in geometry and topology'.