Michael Kesden (UT Dallas) gave a great talk today about black-hole–black-hole binary orbits, and the spin–orbit and spin–spin interactions during inspiral. He showed that he can reduce the dimensionality of the spin interaction problem massively using invariants of the motion, and then obtained a regular, analytic solution for the spin evolution. This new solution will massively speed up post-Newtonian calculations of orbits and gravitational-wave waveforms and also will deliver new insight about relativistic dynamics. Along those lines, he found new resonances (spin-evolution resonances with the orbit) and three qualitatively different behaviors of the spin vectors in three different regimes of spin magnitude and alignment. It is also very related to everything I am teaching this semester!