Complete Monotonicity and Dual Volumes of Positive Geometries - Lecture 1

This lecture is the first in a series exploring "Complete Monotonicity and Dual Volumes of Positive Geometries" presented by Prashanth Raman at the International Centre for Theoretical Sciences. Delve into the mathematical foundations connecting positive geometry to scattering amplitudes and cosmological correlators as part of the program "Positive Geometry in Scattering Amplitudes and Cosmological Correlators." The lecture bridges two distinct disciplines: mathematical aspects of scattering amplitudes and cosmology, exploring recent developments including unitarity methods, recursion relations, worldsheet models, bootstrap methods, and connections to positive geometry, positive Grassmannian, Associahedron, and the Amplituhedron. Learn how these advanced mathematical concepts are pushing toward a reformulation of the perturbative S-matrix using novel principles, while discovering parallel structures observed in cosmological correlators that describe our Universe's fundamental physics.