Dynamics and transients around supermassive black holes

Most galaxies host a supermassive black hole (SMBH) at their center, surrounded by a dense cluster of stars and stellar-mass black holes. In this talk, we discuss how scatterings and gravitational wave emission shape the stellar distribution around these SMBHs, driving a range of transients such as tidal disruption events, X-ray quasi-periodic eruptions, and gravitational wave sources. Our focus will be on extreme mass-ratio inspirals — the mergers of stellar-mass black holes with SMBHs. We calculate their formation rate and predict the number of events that will be detectable by LISA, the upcoming space-based gravitational wave observatory.