Higher enveloping algebras and configuration spaces of manifolds

I will describe a construction providing Lie algebras with enveloping algebras over the operad of little $n$-dimensional
disks for any $n$. These algebras enjoy a combination of good formal properties and computability, the latter afforded
by a Poincaré-Birkhoff-Witt type result. The main application pairs this theory with the theory of factorization homology
in a study of the rational homology of configuration spaces, leading to a wealth of computations, improvements of classical results, and a combinatorial proof of homological stability.