Title: Precision Kerr Black Hole Dynamics from Scattering Amplitudes

Abstract: Scattering amplitudes have emerged as a powerful tool for computing classical observables in two-body gravitational dynamics. In this talk, I will present new progress in applying these methods to Kerr black hole scattering. A central theme is the treatment of Kerr black holes as point particles in fixed-spin representations, which introduces a subtle mixing of quantum and classical data associated with the spin Casimir S^2. We resolve this ambiguity using our spin interpolation method. Building on this framework, we compute the classical two-loop amplitude through quartic order in spin, enabling the extraction of physical (non-aligned spin) observables such as the linear and angular impulses via covariant Dirac brackets. Remarkably, the resulting amplitude exhibits a spin-shift symmetry: it remains invariant under shifts of the black hole spin by the momentum transfer in the scattering process. Finally, we combine the radiation-reaction result proposed by Alessio and Di Vecchia with the Dirac bracket formalism to obtain radiation-reaction contributions to observables at all orders in spin, going beyond the aligned-spin limit. Our results advance the state of the art in the understanding of spinning binary dynamics in general relativity and demonstrates the power and simplicity of the Dirac bracket approach for relating scattering amplitudes to classical observables.