High-Energy physics at the frontier with mathematics
The discovery of the Higgs boson at the LHC has confirmed the Standard Model of Particle Physics up to the highest energies ever tested in a laboratory. The Standard Model is based on a rich mathematical framework, Quantum Field Theory. Among the most powerful instruments to extract precise theoretical predictions for physical observables in Quantum Field Theory are the so-called scattering amplitudes: remarkably involved mathematical objects which encapsulate the probabilities of particle collisions. The calculation of scattering amplitudes remains an outstanding mathematical problem, which has become the object of intense study both from physicists and mathematicians. In the last decade many unexpected connections have been discovered between distant fields such as number theory, algebraic geometry, string theory and particle physics. These apparently formal developments have proven to be decisive to investigate fundamental physics at unprecedented energies and precisions.   HighPHun positions itself in this exciting context and has two major and intertwined goals:   1- To extend our understanding of the mathematical properties of scattering amplitudes and, in this way, help to unravel long-standing puzzles in perturbative Quantum Field Theory.   2- To perform currently out-of-reach calculations in the Standard Model and help to uncover precious details about the most fundamental laws of physics.  At the heart of HighPHun is the ambitious goal of combining cutting-edge ideas in physics and mathematics to solve outstanding problems in high-energy physics. The synergies generated by this project will, on the one hand, extend the reach of the LHC and of future colliders searches for elusive signs of New Physics and, on the other, help us develop a deeper mathematical understanding of Quantum Field Theory.