  Electromagnetic observations over the last 15 years have yielded a growing
appreciation for the importance of supermassive black holes (SMBH) to the
evolution of galaxies, and for the intricacies of dynamical interactions in our
own Galactic center. Here we show that future low-frequency gravitational wave
observations, alone or in combination with electromagnetic data, will open up
unique windows to these processes. In particular, gravitational wave detections
in the 10^{-5}-10^{-1} Hz range will yield SMBH masses and spins to
unprecedented precision and will provide clues to the properties of the
otherwise undetectable stellar remnants expected to populate the centers of
galaxies. Such observations are therefore keys to understanding the interplay
between SMBHs and their environments.
