  We give a method for computing factorization homology of $\oper{E}_n$-algebra
using as an input an algebraic version of higher Hochschild homology due to
Pirashvili. We then show how to compute higher Hochschild homology and
cohomology when the algebra is \'etale in a sense that we make precise. As an
application, we compute higher Hochschild cohomology of the Lubin-Tate ring
spectrum.

Algebraic Topology