Title: Calabi–Yau Categories and Quivers with Superpotential

Abstract: In this talk, I will discuss a noncommutative analogue of a (smooth, compact) Calabi–Yau manifold. As a concrete local model for this analogue, I construct a quiver with superpotential. The definitions and the construction are explained through detailed B-side examples. If time permits, I will also explain the general pattern underlying this construction, known as Koszul duality.