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Applications of intersection theory and gradients : From maximum likelihood to chromatic polynomials

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2025

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Seynnaeve, Tim

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https://doi.org/10.4171/ecr/22/4
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BÜRGISSER, Peter, Hrsg., Gavril FARKAS, Hrsg., Christian HAASE, Hrsg.. Varieties, Polyhedra, Computation. Berlin: EMS Press, 2025, S. 95-141. EMS Series of Congress Reports. ISBN 978-3-98547-096-9. Verfügbar unter: doi: 10.4171/ecr/22/4

Zusammenfassung

In recent years, we have witnessed tremendous applications of algebraic intersection theory to branches of mathematics, that previously seemed very distant. In this article we review some of them. Our aim is to provide a unified approach to the results, e.g., in the theory of chromatic polynomials (work of Adiprasito, Huh, Katz), maximum likelihood degree in algebraic statistics (Drton, Manivel, Monin, Sturmfels, Uhler, Wiśniewski), Euler characteristics of determinental varieties (Dimca, Papadima), characteristic numbers (Aluffi, Schubert, Vakil) and the degree of semidefinite programming (Bothmer, Nie, Ranestad, Sturmfels). Our main tools come from intersection theory on special varieties called the varieties of complete forms (De Concini, Procesi, Thaddeus) and the study of Segre classes (Laksov, Lascoux, Pragacz, Thorup).

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510 Mathematik

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ISO 690DINU, Rodica, Mateusz MICHALEK, Tim SEYNNAEVE, 2025. Applications of intersection theory and gradients : From maximum likelihood to chromatic polynomials. In: BÜRGISSER, Peter, Hrsg., Gavril FARKAS, Hrsg., Christian HAASE, Hrsg.. Varieties, Polyhedra, Computation. Berlin: EMS Press, 2025, S. 95-141. EMS Series of Congress Reports. ISBN 978-3-98547-096-9. Verfügbar unter: doi: 10.4171/ecr/22/4
BibTex
@incollection{Dinu2025-12-10Appli-75553,
  title={Applications of intersection theory and gradients : From maximum likelihood to chromatic polynomials},
  year={2025},
  doi={10.4171/ecr/22/4},
  isbn={978-3-98547-096-9},
  address={Berlin},
  publisher={EMS Press},
  series={EMS Series of Congress Reports},
  booktitle={Varieties, Polyhedra, Computation},
  pages={95--141},
  editor={Bürgisser, Peter and Farkas, Gavril and Haase, Christian},
  author={Dinu, Rodica and Michalek, Mateusz and Seynnaeve, Tim}
}
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