Title: Black hole mergers in AGN disks and Few-body code SpaceHub

Abstract: Active galactic nucleus (AGN) disks may be important sites for stellar mass binary black hole (BBH) mergers, but the detailed processes that lead to a BBH merger in an AGN disk are not yet well-constrained. Binary formation in AGN disks could be extremely efficient due to the so-called migration trap in AGN disks. Dynamical encounters in the migration trap could play a critical role in merging binaries in the AGN channel. I will show via numerical experiments with the high-accuracy, high-precision code SpaceHub that broken symmetry in dynamical encounters in AGN disks can lead to an asymmetry between prograde and retrograde BBH mergers. An asymmetric distribution of mass-weighted projected spin of the BBH mergers that is unlikely to be predicted in other merger channels will show in the AGN merger channel. I will also present the open source few-body gravity integration toolkit SpaceHub. SpaceHub offers a variety of algorithmic methods, which we show out-perform other methods in the literature and allow for fast, precise and accurate computations to deal with few-body problems ranging from interacting black holes to planetary dynamics. With algorithmic regularization, chain algorithm, active round-off error compensation and a symplectic kernel implementation, SpaceHub is the fastest and most accurate tool to treat black hole dynamics with extreme mass ratios, extreme eccentricities and very close encounters.