## Prof. Grigoriy Blekherman

### October 14, 2020 @ 4:15 pm - 5:30 pm

**Title:** Nonnegative Polynomials and Sums of Squares

**Abstract:** Is *x*^{4}-2x^{3}+7x^{2}-2x+1 nonnegative for any value of *x*? One way of showing that this holds is by writing *x*^{4}-2x^{3}+7x^{2}-2x+1=1/2(x^{2}-3x+1)^{2}+1/2(x^{2}+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.