Elementary recursive complexity results in real algebraic geometry (Women in Mathematics)

Abstract

I shall discuss two important results in real algebraic geometry - quantifier elimination, proving that the projection of a semi-algebraic set is semi-algebraic - Hilbert 17th problem, proving that a non negative polynomial is always a sum of squares of rational functions from the point of view of effectivity and complexity. The two problems look at first sight totally un related at all but it turns out that modern computer algebra techniques play a key role in proving elementary recursive complexity results for both these problems.