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Sums of three squares and Noether-Lefschetz loci
Multi angle
Authors : Benoist, Olivier (Author of the conference)
CIRM (Publisher )
11E25 - Sums of squares and representations by other particular quadratic forms
14D07 - Variation of Hodge structures
14M12 - Determinantal varieties
14Pxx - Real algebraic and real analytic geometry
CIRM (Publisher )
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Abstract :
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.
MSC Codes : 11E25 - Sums of squares and representations by other particular quadratic forms
14D07 - Variation of Hodge structures
14M12 - Determinantal varieties
14Pxx - Real algebraic and real analytic geometry
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 21/09/2017 Conference Date : 21/09/2017 Subseries : Research talks arXiv category : Algebraic Geometry ; Applications Mathematical Area(s) : Algebraic & Complex Geometry ; Number Theory Format : MP4 (.mp4) - HD Video Time : 01:06:05 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2017-09-21_Benoist.mp4 
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Information on the Event
Event Title : Perspectives in real geometry / Perspectives en géométrie réelleEvent Organizers : Brugallé, Erwan ; Itenberg, Ilia ; Shustin, Eugenii Dates : 18/09/2017 - 22/09/2017 Event Year : 2017 Event URL : http://conferences.cirm-math.fr/1782.html
Citation Data
DOI : 10.24350/CIRM.V.19222303Cite this video as: Benoist, Olivier (2017). Sums of three squares and Noether-Lefschetz loci. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19222303 URI : http://dx.doi.org/10.24350/CIRM.V.19222303 |
See Also
- [Post-edited] Expected topology of a random subcomplex in a simplicial complex / Author of the conference Welschinger, Jean-Yves.
- [Multi angle] Real curves and a Klein TQFT / Author of the conference Georgieva, Penka.
- [Multi angle] On real algebraic knots and links / Author of the conference Orevkov, Stepan.
- [Multi angle] Complex torus, its good compactifications and the ring of conditions / Author of the conference Khovanskii, Askold.
Bibliography
- Benoist, O. (2017). Sums of three squares and Noether-Lefschetz loci.
