Sums of Squares Method in Geometry, Combinatorics and Optimization

The study of nonnegative polynomials and sums of squares is a classical area of real algebraic geometry dating back to Hilbert's 17th problem. It also has rich connections to real analysis via duality and moment problems. In the last 15 years, sums of squares relaxations have found a wide array of applications from very applied areas (e.g., robotics, computer vision, and machine learning) to theoretical applications (e.g., extremal combinatorics, theoretical computer science).