Complete quadrics : Schubert calculus for Gaussian models and semidefinite programming

Kurzanzeige
dc.contributor.authorManivel, Laurent
dc.contributor.authorMichalek, Mateusz
dc.contributor.authorMonin, Leonid
dc.contributor.authorSeynnaeve, Tim
dc.contributor.authorVodicka, Martin
dc.date.accessioned2024-06-26T09:46:06Z
dc.date.available2024-06-26T09:46:06Z
dc.date.issued2023-05-03
dc.description.abstractWe 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.
dc.description.versionpublisheddeu
dc.identifier.doi10.4171/jems/1330
dc.identifier.ppn1892254999
dc.identifier.urihttps://kops.uni-konstanz.de/handle/123456789/70261
dc.language.isoeng
dc.rightsterms-of-use
dc.rights.urihttps://rightsstatements.org/page/InC/1.0/
dc.subjectComplete quadrics Lascoux coefficients
dc.subjectML-degree
dc.subjectSDP-degree
dc.subjectLascoux polynomials
dc.subject.ddc510
dc.titleComplete quadrics : Schubert calculus for Gaussian models and semidefinite programmingeng
dc.typeJOURNAL_ARTICLE
dspace.entity.typePublication
kops.citation.bibtex
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  doi={10.4171/jems/1330},
  title={Complete quadrics : Schubert calculus for Gaussian models and semidefinite programming},
  number={8},
  volume={26},
  issn={1435-9855},
  journal={Journal of the European Mathematical Society},
  pages={3091--3135},
  author={Manivel, Laurent and Michalek, Mateusz and Monin, Leonid and Seynnaeve, Tim and Vodicka, Martin}
}
kops.citation.iso690MANIVEL, Laurent, Mateusz MICHALEK, Leonid MONIN, Tim SEYNNAEVE, Martin VODICKA, 2023. Complete quadrics : Schubert calculus for Gaussian models and semidefinite programming. In: Journal of the European Mathematical Society. EMS Press. 2023, 26(8), S. 3091-3135. ISSN 1435-9855. eISSN 1435-9863. Verfügbar unter: doi: 10.4171/jems/1330deu
kops.citation.iso690MANIVEL, Laurent, Mateusz MICHALEK, Leonid MONIN, Tim SEYNNAEVE, Martin VODICKA, 2023. Complete quadrics : Schubert calculus for Gaussian models and semidefinite programming. In: Journal of the European Mathematical Society. EMS Press. 2023, 26(8), pp. 3091-3135. ISSN 1435-9855. eISSN 1435-9863. Available under: doi: 10.4171/jems/1330eng
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