Supermassive Black Hole Modeling for the Low-Frequency Gravitational-Wave Era

Supermassive black hole (SMBH) binaries are extremely powerful sources of gravitational waves (GWs) at ~ nanoHertz to milliHertz frequencies. The detection of such GWs with pulsar timing arrays (PTAs) may be imminent, and in the coming years, the Laser Interferometer Space Antenna (LISA) could detect SMBH merger events. I will summarize recent work using cosmological hydrodynamics simulations to constrain the formation of SMBH "seeds" in the early Universe, which will be key for understanding the LISA source population. I will also describe recent progress in modeling the dynamics and fueling of SMBHs, particularly in merging galaxies. These models enable new predictions of GW and multi-messenger source populations for the dawning era of low-frequency GW astrophysics