Kontsevich’s formality theorem in deformation theory asserts that the Hochschild-Kostant-Rosenberg map lifts to a quasi-isomorphism of homotopy Gerstenhaber algebras between polyvector fields and polydifferential operators. By exhibiting the sheaf of polydifferential operators as a universal enveloping algebra, this can be interpreted as a type of Duflo isomorphism. In this talk, I will present my work towards understanding this geometric Duflo isomorphism in the context of ∞-operads and higher centers. In particular, I will explain how higher centers can be used to equip the Hochschild cochain complex with a universal property.