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We establish connections between: the maximum likelihood degree (ML-degree)for linear concentration models, the algebraic degree of semidefiniteprogramming (SDP), and Schubert calculus for complete quadrics. We prove aconjecture by Sturmfels and Uhler on the polynomiality of the ML-degree. Wealso prove a conjecture by Nie, Ranestad and Sturmfels providing an explicitformula for the degree of SDP. The interactions between the three fields shednew light on the asymptotic behaviour of enumerative invariants for the varietyof complete quadrics. We also extend these results to spaces of generalmatrices and of skew-symmetric matrices.

Complete quadrics: Schubert calculus for Gaussian models and semidefinite programming