Equivariant completion of bicategories

Dividing out by the action of a group on some algebraic structure is a ubiquitous construction. In topological quantum field theory, where it appears in "orbifolding a symmetry", this leads to a natural generalisation called "equivariant completion". Equivariant completion is a simple, purely categorical construction that can uncover unexpected new relations. We shall introduce the basic ideas of this theory, and then apply it to produce equivalences between categories of matrix factorisations, derived categories of path algebras of Dynkin quivers, and, if time permits, remark on further applications to homological link invariants and Ginzburg algebras.