Loop Corrections from the Theory of Motives

The interactions between the elementary particles are encoded into a set of mathematical quantities called scattering amplitudes. Consequently, they are key to making predictions for physical observables that match the precision achieved by current and future high-energy experiments. Due to our ignore of the mathematics involved, computing loop quantum corrections to scattering amplitudes is still a major challenge today, and calls for innovative and groundbreaking new techniques.Over the last decade, a new field of research that studies scattering amplitudes through the lens of a certain branch of modern mathematics, the so-called theory of motives, has led to breakthroughs in how we compute loop quantum corrections. LoCoMotive will bring the connection between scattering amplitudes and modern mathematics to the next level. It will investigate in detail what the theory of motives teaches us about the structure of scattering amplitudes. Its final aim is to achieve a global change of perspective on the mathematical underpinnings of the laws of nature and develop novel computational techniques for scattering amplitudes that are currently beyond reach of conventional state-of-the-art technology. Inspired by cutting-edge research in seemingly-disconnected areas in mathematics and physics, LoCoMotive will 1) perform the computations needed to reveal how concepts from geometry govern the fundamental interactions.2) play a decisive role in providing the theoretical predictions needed for the LHC and future collider experiments. 3) act as a catalyser for new research in mathematics.To sum up, LoCoMotive is a timely proposal with a unique multi-disciplinary character, whose results will bridge a gap between formal theory and concrete phenomenological results. It will have a major impact on formal aspects of quantum field theory and possibly even pure mathematics, and provide highly-needed theoretical predictions for the LHC experiments.