Sums of three squares and Noether-Lefschetz loci
Apparaît également dans la collection : Perspectives in real geometry / Perspectives en géométrie réelle
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.
![$k$-sum free sets in $[0,1]$](/media/cache/video_light/uploads/video/2015-09-10_de_Roton-video--19cf70874d3c5af7378c268cab865b06.jpg)
