My research strives towards obtaining better mathematical descriptions for high-energy collisions (scattering amplitudes) between elementary particles or even strings. New mathematical formulations of fundamental processes can lead to a better understanding of the theories that describe our universe: e.g. the theory of gravity and other established theories known as gauge theories — describing the strong and electroweak forces of the Standard Model of particle physics. By studying the mathematical details of scattering amplitudes in these theories, I have found that there exists an underlying Lie algebra that controls the kinematical variables. However, as of today, no complete mathematical description of this algebra is known. A goal of my research is to find this complete description.