Title: Four Dimensional Polytopes of Minimum Positive Semidefinite Rank
|Affiliation:||University of Waterloo|
For a given polytope the smallest size of a semidefinite extended formulation can be bounded from below by the dimension of the polytope plus one. This talk is about polytopes for which this bound is tight, i.e. polytopes with positive semidefinite (psd) rank equal to their dimension plus one.
I will introduce all necessary concepts, present some known results such as the generalization of Yannakakis' theorem from the linear to positive semidefinite case, and a characterization of slack matrices that correspond to polytopes of psd minimum rank.
In the end, I will speak about a classification of psd minimum polytopes in dimension four.
Joint work with Gouveia, Robinson and Thomas.