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This lecture is the first in a series on "From Positive Geometries to Scattering Amplitudes" delivered by Alok Laddha at the International Centre for Theoretical Sciences. Explore the fascinating intersection between mathematical structures and particle physics as part of the program "Positive Geometry in Scattering Amplitudes and Cosmological Correlators." Organized by renowned physicists Nima Arkani-Hamed, Johannes Henn, Suvrat Raju, and Jaroslav Trnka, this lecture contributes to a workshop bringing together experts from scattering amplitudes and cosmology fields. Discover how recent advances in perturbative on-shell scattering amplitudes—including unitarity methods, recursion relations, and connections to positive geometry—are pushing toward a revolutionary reformulation of the perturbative S-matrix. Learn about the remarkable parallel structures observed in cosmological correlators and how these connections are bridging seemingly disparate areas of theoretical physics.
