Master thesis defense by Daniel Brammer

Title: Classifying Geometries of Four-Loop Post-Minkowskian Feynman Integrals

Abstract: The recent detection of gravitational waves has opened a new frontier in understanding the universe, particularly in the dynamics of inspiraling binary mergers of black holes and neutron stars. This thesis defense explores the application of modern quantum field theory techniques to improve the precision modeling required for next-generation gravitational-wave detectors. By examining Feynman integrals at higher-loop orders in the post-Minkowskian (PM) expansion and classifying their underlying geometric structures, including K3 surfaces and Calabi-Yau manifolds, this research contributes to developing tools to aid our ability to compute high-precision classical gravitational observables. These findings enhance our current understanding of the geometric structures that emerge at the fifth order in the PM expansion, which will aid in the precise theoretical modeling necessary for interpreting gravitational-wave signals.