Sums of three squares and Noether-Lefschetz loci | Vidéo | Carmin.tv

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Sums of three squares and Noether-Lefschetz loci

By Olivier Benoist

Appears in collections : Perspectives in real geometry / Perspectives en géométrie réelle, Exposés de recherche

It is a theorem of Hilbert that a real polynomial in two variables that is nonnegative is a sum of 4 squares of rational functions. Cassels, Ellison and Pfister have shown the existence of such polynomials that are not sums of 3 squares of rational functions. In this talk, we will prove that those polynomials that may be written as sums of 3 squares are dense in the set of nonnegative polynomials. The proof is Hodge-theoretic.

Information about the video

Date of recording 21/09/2017
Date of publication 21/09/2017
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.19222303
Cite this video Benoist, Olivier (21/09/2017). Sums of three squares and Noether-Lefschetz loci. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19222303
URL https://dx.doi.org/10.24350/CIRM.V.19222303

Domain(s)

Bibliography

Benoist, O. (2017). Sums of three squares and Noether-Lefschetz loci. <arXiv:1706.02053> - https://arxiv.org/abs/1706.02053

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