Scattering Amplitudes and Novel Approaches to Field Theory

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In any quantum field theory, the S-matrix - which encodes the scattering amplitudes of the theory - is the most fundamental observable. Amplitudes are directly related to cross sections, which are measured at particle accelerators such as the LHC. Hence a thorough study of the S-matrix is of fundamental importance both on a theoretical and experimental side. In recent years, hidden mathematical structures have been unearthed - structures which are completely obscured by standard perturbative methods. These developments have dramatically improved our understanding of the S-matrix and led to the discovery of new symmetries and dualities, which in turn have triggered the development of novel, and highly efficient techniques to compute amplitudes. Remarkably, some of these results are of direct use to the LHC. This project will focus on the most recent and fascinating developments in this rapidly evolving field.