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Description

Mathematics Colloquium.

Speaker: Charu Goel.

Affiliation: IIIT Nagpur.

Date and Time: Wednesday 09 October, 4:00 pm - 5:00 pm.

Venue: Ramanujan Hall, Department of Mathematics.

Title: Nonnegative Polynomials and Sums of Squares

Abstract:
Abstract. Sums of squares representations of polynomials is of fundamental importance in real algebraic geometry and goes back to the 1888 seminal paper of Hilbert. The main theorem in his paper is a full characterisation of all pairs (n,d) for which every nonnegative polynomial of a fixed degree d in a given number of variables n is a sum of squares of polynomials. Ninety years later, Choi and Lam asserted that this characterisation remains unchanged for symmetric forms. In this talk first some key observations and problems related to Hilbert’s theorem will be discussed. We then complete the above assertion of Choi-Lam. Along the way, we shall also discuss briefly how test sets for positivity of symmetric polynomials play an important role in establishing this assertion.

Charu Goel : IIIT Nagpur : Mathematics Colloquium