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Explore the impact of gas-rich environments on low-frequency gravitational waves emitted by supermassive black hole binaries in this 48-minute colloquium presented by Dr. Fatemeh Hossein-Nouri at the Center for Theoretical Physics PAS. Delve into the upcoming Laser Interferometer Space Antenna (LISA) mission and its potential to detect mHz gravitational waves from various astrophysical sources. Examine how accretion disk environments surrounding binary systems in active galactic nuclei (AGN) can influence gravitational wave signals, particularly in Extreme Mass Ratio Inspiral (EMRI) cases. Learn about the phase shift effect in gravitational wave signals and its implications for understanding AGN accretion disk physics. Discover recent research on disk torques and magnetized tori modeling, exploring angular momentum transport and turbulence generated by magnetorotational instability (MRI). Gain insights into the quantification of disk alpha-viscosity and its temporal evolution. Understand how numerical simulation results are applied to estimate relativistic viscous torque and gravitational wave phase shifts caused by MRI-driven turbulence.