Loop Amplitudes in the Scattering Equations Formalism

 I will describe recent progress in the study of scattering amplitudes in gauge theory and gravity at loop level, using the formalism of the scattering equations. The scattering equations relate the kinematics of the scattering of massless particles to the moduli space of the sphere. Underpinned by ambitwistor string theory, this formalism provides new insights into the relation between tree-level and loop-level contributions to scattering amplitudes. In this talk, I will describe results up to two loops on how loop integrands can be constructed as forward-limits of trees. One application is the loop-level understanding of the colour-kinematics duality, a symmetry of perturbative gauge theory which relates it to perturbative gravity.