This talk revolves around two of the most recent remarkable developments of the scattering amplitude domain ; the scattering equation formalism, and the double copy.
The first one is a formalism inspired by Penrose's ideas that expresses all tree-level scattering amplitudes in a remarkably compact way. With collaborators from Oxford, we extended it’s use to loop-level but some conceptual issues prevent to push it further.
The second is a formalism developed by Bern et al. to compute gravity loop integrands as squares of gauge theory integrands, which works to surprising high loop orders but whose origin remains completely mysterious.
I will explain how we use the recently discovered monodromies string higher loop amplitudes to attack both problems and the current point we stand at.
More than the first half of the talk should be a non-technical review. In the second part, I will introduce in a simple way the notion of twisted homologies and mention how it relates to string theory, and both problems above.