Hypersurfaces with large automorphism groups

We find sharp upper bounds on the order of the automorphism group of a hypersurface in complex projective space in every dimension and degree. In each case, we prove that the hypersurface realizing the upper bound is unique up to isomorphism and provide explicit generators for the automorphism group. Similar results were recently proven independently by S. Yang, X. Yu, and Z. Zhu using different methods.