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This lecture, the second in a series on Positive Geometry in Scattering Amplitudes and Cosmological Correlators, explores Complete Monotonicity and Dual Volumes of Positive Geometries presented by Prashanth Raman at the International Centre for Theoretical Sciences. Delve into advanced mathematical concepts connecting perturbative on-shell scattering amplitudes with cosmological correlators. Part of a workshop bringing together experts from scattering amplitudes and cosmology fields, the presentation examines how positive geometry, positive Grassmannian, Associahedron, and the Amplituhedron contribute to reformulating the perturbative S-matrix with new principles. The workshop aims to advance connections between these theoretical physics disciplines, revealing structural similarities between scattering amplitudes and cosmological correlators that capture fundamental aspects of our Universe.
