This review describes the duality between color and kinematics and its applications, with the
aim of gaining a deeper understanding of the perturbative structure of gauge and gravity …

A bstract The search for a theory of the S-Matrix over the past five decades has revealed
surprising geometric structures underlying scattering amplitudes ranging from the string …

A bstract The tree-level S-matrix of Einstein's theory is known to have a representation as an
integral over the moduli space of punctured spheres localized to the solutions of the …

A bstract In a recent note we presented a compact formula for the complete tree-level S-
matrix of pure Yang-Mills and gravity theories in arbitrary spacetime dimension. In this paper …

Several recent developments point to the fact that rational maps from n-punctured spheres to
the null cone of D-dimensional momentum space provide a natural language for describing …

We show that double-copy maps for amplitudes in effective field theory are severely
constrained at four points by self-consistency and locality at six points. The resulting double …

A bstract Recent years have seen a surprising connection between the physics of scattering
amplitudes and a class of mathematical objects—the positive Grassmannian, positive loop …

A bstract We show that string theories admit chiral infinite tension analogues in which only
the massless parts of the spectrum survive. Geometrically they describe holomorphic maps …

A bstract We show that color-kinematics duality is present in tree-level amplitudes of
quantum chromodynamics with massive flavored quarks. Starting with the color structure of …

We present a connection between the physics of cosmological time evolution and the
mathematics of positive geometries, roughly analogous to similar connections seen in the …