Closing the gap in the black hole mass spectrum with new detections of intermediate-mass black holes*

Very little is known about the formation, evolution, and demographics of intermediate-mass black holes (IMBHs). While the classical approach to prove their existence based on the use of optical and infrared data is limited to nearby systems, gravitational wave (GW) missions have the potential to shed light on IMBHs up to the distant Universe. IMBH sources are most likely to be produced in dense stellar environments, where IMBHs can form GW-emitting binaries through dynamical interactions with other compact objects. The intermediate mass-ratio inspiral of a stellar compact remnant into an IMBH is a potential target for multi-band detection, since LISA measurements will alert astronomers of an incoming merger detectable within the next few years by LIGO/Virgo/Kagra, Einstein Telescope, and Cosmic Explorer. I will discuss how the properties of the host stellar environment affect the IMBH dynamics and growth, and characterize the typical GW signal expected for current and upcoming missions, which offer for the first time the opportunity to demonstrate the existence of IMBHs beyond any reasonable doubt and to fill the gap in the BH-mass spectrum. The next decade may bring hundreds of events, promising a spectacular range of new science from stellar evolution to cosmology.