Math & Stats Colloquium: Extension of Hilbert's 1888 theorem to Even Symmetric Forms

Title:
Extension of Hilbert's 1888 theorem to Even Symmetric Forms

Guest:
Professor Salma Kuhlmann
University of Konstanz, Germany

Location:
ARTS 108

Day and Time:
September 12 2014, 3:30 PM

Abstract:

A multivariate real form (homogeneous polynomial with real coecients) is
said to be positive semi-denite (PSD) if it is non-negative when evaluated at
every tuple of real numbers.

If a form is a sum of squares of real forms (SOS) it is clearly PSD.
For forms of degree 2d in n-variables, Hilbert's 1888 celebrated Theorem characterized
the pairs (n, 2d) for which the cones of SOS and that of PSD forms
coincide.

Later, Choi, Lam and Reznick re-considered Hilbert's 1888 under the additional
assumption that the forms under consideration are symmetric (i.e. invariant
under the action of the symmetric group).

In this talk, we will rst present the work of Hilbert, Choi-Lam-Reznick, and a
generalization thereof to the case of {it even} symmetric forms. The latter
results are obtained in the Dissertation of my PhD student Charu Goel.

POSTER HERE!