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This lecture is the first in a series on Nonlinear Algebra for Physics delivered by Dmitrii Pavlov at the International Centre for Theoretical Sciences as part of the program "Positive Geometry in Scattering Amplitudes and Cosmological Correlators." Explore the mathematical foundations that connect perturbative on-shell scattering amplitudes with cosmological correlators. The lecture delves into how nonlinear algebraic methods contribute to understanding positive geometry, positive Grassmannian, Associahedron, and the Amplituhedron—concepts that are pushing toward a reformulation of the perturbative S-matrix using novel principles. Part of a workshop designed to bridge two different disciplines in theoretical physics, this 84-minute session establishes fundamental concepts that will help advance connections between scattering amplitudes and the physics of our Universe.
