As part of a summer school associated to the Hausdorff Institute for Mathematics Program on Combinatorial Optimization, I will be giving some lectures on “Semi-definite extended formulations and sums of squares.”
I wanted to post here a draft of the lecture notes. These extend and complete the series of posts here on non-negative and psd rank and lifts of polytopes. They also incorporate many corrections, and have exercises of varying levels of difficulty. The bibliographic references are sparse at the moment because I am posting them from somewhere in the Adriatic (where wifi is also sparse).