MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV ( that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint

Complete quadrics: Schubert calculus for Gaussian models and semidefinite programming

Laurent Manivel, Mateusz Michałek, Leonid Monin, Tim Seynnaeve and Martin Vodička


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.

Dec 2, 2020
Dec 24, 2020
MSC Codes:
62R01, 14M17, 14N10
maximum likelihood degree, degree of semidefinite programming, complete quadrics, enumerative geometry, polynomiality

Related publications

2023 Repository Open Access
Laurent Manivel, Leonid Monin, Mateusz Michałek, Tim Seynnaeve and Martin Vodička

Complete quadrics : Schubert calculus for Gaussian models and semidefinite programming

In: Journal of the European Mathematical Society, (2023)