Shengding Sun: Semidefinite relaxations and sum of squares hierarchy for quadratic programming on roots of unity

Discrete complex quadratic programming generalizes binary quadratic programming, where each decision variable is replaced by complex m-roots of unity. We will talk about how various results and techniques for binary quadratic programming can be generalized to this problem, and the difficulties that are unique to the complex setting. We will focus on semidefinite relaxations and the sum of squares hierarchy, including the result by (Al-Sulami, Fawzi, S.) that the level floor(n/2)+1 of an appropriately defined sum of squares hierarchy is always exact.