In the past decades and especially the last one, powerful new tools and remarkable new structures for perturbative scattering amplitudes in Quantum Field Theory (QFT) have been discovered. Apart from playing a prominent role in high-energy particle physics, these developments have important implications in a wide range: from string perturbation theory to multi-loop calculations in (super)-gravity, from new mathematics to all-loop amplitudes in N=4 Supersymmetric Yang-Mills Theory (SYM). In this talk, the speaker will review some recent progress, with focus on two topics: (1) a string-inspired new formulation for amplitudes in gauge theories and gravity, and double-copy between them; (2) new geometric structures underlying amplitudes which may hint at a “theory at infinity” for S-matrices.
