### Speaker

### Description

I review the description of perturbative quantum field theory in terms of homotopy algebras, which provides a unifying picture for actions and scattering amplitudes. In this picture, each field theory is encoded in an L∞-algebra, a generalization of a differential graded Lie algebra, and any extra structure on scattering amplitudes amounts to a homotopy algebraic refinement of the L∞-algebra. I discuss in detail the case colour-kinematics duality, where the refinement is captured by a generalization of homotopy BV-algebras. This perspective is well-motivated from string theory and also yields an explicit description of the double copy. It provides a clean mathematical characterization of colour-kinematics duality and identifies the kinematical algebra for any CK-dual field theory.