Factorization algebras provide a flexible language for describing the observables of a perturbative QFT, as shown in joint work with Kevin Costello. Those constructions extend to a manifold with boundary for a special class of theories. I will discuss work with Eugene Rabinovich and Brian Williams that includes, as an example, a perturbative version of the correspondence between chiral ${\rm U}(1)$ currents on a Riemann surface and abelian Chern-Simons theory on a bulk 3-manifold, but also includes a systematic higher dimensional version for higher abelian CS theory on an oriented smooth manifold of dimension $4n+3$ with boundary a complex manifold of complex dimension $2n+1$. Given time, I will discuss how this framework leads to a concrete construction of the center of higher enveloping algebras of Lie algebras, in work with Greg Ginot and Brian Williams.