The higher Morita category of $E_n$-algebras

I will discuss a construction of a higher category of $E_n$-algebras and iterated bimodules, generalizing the classical bicategory of algebras and bimodules. This leads to generalizations of the Picard and Brauer groups, which have been studied in stable homotopy theory as interesting invariants of ring spectra, and should also lead to an "algebraic" construction of factorization homology as an extended topological quantum field theory.