We establish connections between: the maximum likelihood degree (ML-degree) for linear concentration models, the algebraic degree of semidefinite programming (SDP), and Schubert calculus for complete quadrics. We prove a conjecture by Sturmfels and Uhler on the polynomiality of the ML-degree. We also prove a conjecture by Nie, Ranestad and Sturmfels providing an explicit formula for the degree of SDP. The interactions between the three fields shed new light on the asymptotic behaviour of enumerative invariants for the variety of complete quadrics. We also extend these results to spaces of general matrices and of skew-symmetric matrices.

翻译：我们建立了线性浓度模型的最大概率度(ML-度)、半确定性编程的代数度(SDP)和完全四分法的舒伯特微积分之间的联系。我们证明了Sturmfels和Uhler对多角度ML-度的推测。我们还证明了Nie、Ranestad和Sturmfels的推测,为SDP的程度提供了明确的公式。这三个领域之间的相互作用为各种完整的四分法的统计性变量的无症状行为提供了新的线索。我们还将这些结果扩大到一般矩阵和Skew对称矩阵的空间。