Binary black hole merger: symmetry and the spin expansion

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Two spinning black holes emit gravitational waves as they orbit, and eventually merge to form a single black hole. How do the properties of the final black hole depend on those of the initial black holes? This is a classic problem in general relativity, with implications for astrophysics, cosmology, and gravitational wave detection. I will describe the rapid numerical and theoretical progress over the past two years, and discuss some open questions and future directions.