This project aims to explore an exciting discovery in mathematical physics, a new algebraic approach to perturbative gauge theory, the colour/kinematics duality, which also provides a connection between gauge theory and gravity. This duality says that the quantum-mechanical amplitudes for particle scattering in gauge theory depend on the momenta and polarisation of the scattered particles (kinematics) in a way that mirrors the dependence on the “colour”, the internal degree of freedom of gauge theories. Kinematics and colour appear, at first sight, in a very different manner, so this strongly suggests that the traditional methods of quantum field theory give us a very limited understanding of gauge theory amplitudes, and many recent results have strengthened this idea. The colour/kinematics duality has the potential to provide new connections between mathematical physics and other areas of mathematics, such as differential and algebraic geometry, twistor theory and graph theory. This proposal is perfectly suited to the expertise of the Mathematical Physics Group of the Mathematical Institute of the University of Oxford, which is the host institution for this project, and to my own research experience across different subjects in mathematical physics, from general relativity and string theory to scattering amplitudes.