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This lecture is the second installment in the "From Positive Geometries to Scattering Amplitudes" series delivered by Alok Laddha at the International Centre for Theoretical Sciences. Explore the mathematical foundations connecting positive geometry to scattering amplitudes as part of the "Positive Geometry in Scattering Amplitudes and Cosmological Correlators" program. 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, worldsheet models, and connections to positive geometry—are pushing toward a reformulation of perturbative S-matrix using novel principles. The lecture also examines how similar structures appear in cosmological correlators, bridging two seemingly distinct areas of theoretical physics.
