Atypicality is a fundamental combinatorial invariant for simple supermodules
of a basic Lie superalgebra. Boe, Nakano, and the author gave a conjectural
geometric interpretation of atypicality via support varieties. Inspired by low
dimensional topology, Geer, Patureau-Mirand, and the author gave a
generalization of the Kac-Wakimoto atypicality conjecture. We prove both of
these conjectures for the Lie superalgebra osp(m|2n).