Seeing the Hidden Geometry in Scattering Amplitudes

Scattering processes are central to how we probe nature, from the act of seeing to high-energy particle collisions at the LHC that reveal fundamental physics at the smallest scales. The standard framework for computing scattering amplitudes relies on Feynman diagrams and rules. While conceptually straightforward, such calculations are often technically involved. Remarkably, however, the final results for scattering amplitudes frequently exhibit striking simplicity. This unexpected simplicity has driven the development of new methods for computing scattering amplitudes and has inspired a reformulation of the subject in terms of positive geometry. In this approach, scattering amplitudes are derived from underlying geometric structures, bypassing Feynman diagrams and making physical properties manifest through geometric principles. The most notable successes of this program so far have been in theories of massless particles with supersymmetry. In this talk, I will discuss recent progress toward extending these ideas to amplitudes involving massive particles and to theories without supersymmetry.