Scattering Amplitudes and QFT Insight

The calculation of scattering amplitudes provides an invariant window into the physical dynamic content of relativistic quantum �field theory. Yet with traditional methods, for empirically relevant theories, these calculations incur a factorial complexity for higher-multiplicity (number of external particles in a given scattering event) or higher loop-order (related to the order of quantum corrections). If we aspire to collapse the theoretical uncertainty obfuscating potentially new physics, this complexity challenge necessitates a revolution in our actual understanding. Similarly if we aspire to understand deeper structure as to how classical notions of space and time may emerge from something more fundamentally quantum, we confront a similar barrier with respect to apprehending the physical content of gauge and gravity theories in concrete formally approachable limits. Novel approaches like the color-kinematics duality and the associated double-copy construction have the possibility to drastically simplify the situation and relate both gauge and gravity theory predictions to a much smaller kernel of invariant kinematic data. This proposal aims to perform strategic ground-breaking calculations in gauge and gravity theories towards identifying and exploiting universal structure. These projects will, through direct calculation, engage formal questions like the ability of point-like quantum �field theory to describe the evolution of the universe gravitationally. Of necessity, this will involve pushing the boundary of the complexity of gauge theory predictions we can extract from our theories|absolutely relevant to higher-order gluonic processe at current and next-generation colliders, calculations of unthinkable complexity even a few years ago. The empirical impact of this new understanding need not stop at collider pheomenology. Leveraging the intimate relations between gauge and gravity predictions, this proposal additionally looks to address|in a particle physics framework|fundamental challenges at the interface between QFT amplitudes analysis and next generation gravitational wave science as well as precision cosmology. Specifi�c Projects: All order in mass-dimension higher-derivative local operator amplitudes in Gauge and Gravity Theory at tree-level. Amplitude calculations towards UV behavior of 6-loops in maximally supersymmetric Gauge and Gravity Theory. Double-copy of Classical Instantons from Gauge Theory to Gravity. Higher-Loop Order scattering calculations relevant to classical black hole scattering involving radiation Identifying gauge theory solutions that double-copy to in infationary cosmology.