seminario Blekherman
Greg Blekherman (UC San Diego, California)
Positive Gorenstein Ideals
Abstract: A multivariate real polynomial p is nonnegative if p(x) is at
least 0 for all x in R^n. I will review the history and motivation behind
the problem of representing nonnegative polynomials as sums of squares. Such
representations are of interest for both theoretical and practical
computational reasons. I will explain that the difference between
nonnegative polynomials and sums of squares comes from Gorenstein ideals
with special structure, which I will call positive Gorenstein ideals.
Although the problem of nonnegative polynomials and sums of squares retains
real flavor, this makes it amenable to the more familiar tools from complex
algebraic geometry and commutative algebra. I will present some applications
of these ideas.