Commutative Algebra Seminar
Justin Chen
Brown University
Sums of squares, Hankel index, and almost real rank
Abstract: The difference between nonnegative polynomials and sums of
squares is an important topic in real algebraic geometry, and the
Hankel index of a variety is a natural (but subtle) invariant that
quantifies this difference. Surprising connections were found between
the Hankel index and the commutative algebra of the variety, namely the
N_{2,p} property of linear syzygies for the free resolution - although
this only provides half the story. For curves of almost minimal degree,
we complete the picture, by determining the Hankel index in terms of a
new rank called almost real rank, which interpolates between real
(Waring) rank and complex border rank. This is joint work with Greg
Blekherman and Jaewoo Jung.
Wednesday November 10, 2021 at 3:00 PM in Zoom