Title: Nonnegative Polynomials and Sums of Squares
Abstract: Is x4-2x3+7x2-2x+1 nonnegative for any value of x? One way of showing that this holds is by writing x4-2x3+7x2-2x+1=1/2(x2-3x+1)2+1/2(x2+x+1)2. Studying the relationship between non-negativity and sums of squares has a distinguished history in mathematics starting with work of David Hilbert and Hilbert’s 17th problem. I will discuss the history and some modern applications of sums of squares in optimization and combinatorics.
Prof. Blekherman is on the Mathematics faculty at Georgia Tech; he also is an advocate for Georgia Tech’s internationally renown Algorithms, Combinatorics and Optimization (ACO) graduate program.