## Details

Current gravitational-wave detectors are being upgraded, and plans are developing for future detectors with greater sensitivity over broader frequency bands. As instruments improve and develop, more cycles of sources’ gravitational waveforms will be measured with greater signal to noise ratio. Such higher fidelity measurements promise to teach us more about their sources and the nature of strong-field gravity — but only if theoretical modeling of these waves is able to match advances in the detectors. As we measure waveforms with better precision, the likelihood increases that systematic modeling errors will affect inferences about what we measure. In this talk, I will survey recent progress modeling waveforms from small-mass binaries. Such binaries, which exactly describe important low-frequency gravitational wave sources, also serve as a limit of the more general binary problem that can be modeled with very high precision. I will discuss the outstanding progress that has been made on this problem in recent years, and how what we learn in this limit can be combined with other binary modeling techniques to advance modeling for relativistic binaries in general.