Georgia Institute of Technology College of Sciences

We study the problem of computing the convex hull of a set $S \subseteq \mathbb{R}^n$ defined by three quadratic inequalities. A simple way to generate inequalities valid on $S$ is to take nonnegative linear combinations, called aggregations, of the defining inequalities. We study the set defined by aggregations using topological duality results for quadratic inequalities. In the case of three quadratic inequalities, this relates aggregations to an algebraic curve. This viewpoint allows us to find new cases for which the convex hull of $S$ can be recovered by aggregations. Joint work with Greg Blekherman.