Hilbert's 17th Problem


March 9, 2018 | 2:30 - 3:30 p.m.


Campbell Hall 443


Daniel Perrucci, Universidad de Buenos Aires, Argentina


Hilbert's 17th problem concerns the representation of a non-negative multivariate real polynomial as a sums of squares of rational functions. More precisely, the question posed by Hilbert is if such a representation always exists, providing a certificate of its non-negativity. This question was affirmatively answered by Emil Artin in 1927. In recent years there has been a renewed interest in this kind of certificates. In this talk we will survey some results in this area.