Spectrahedral shadows
arXiv:1612.07048
Abstract
We show that there are many (compact) convex semi-algebraic sets in euclidean space that do not have a semidefinite representation. This gives a negative answer to a question by Nemirovski, resp. it shows that the Helton-Nie conjecture is false.
ver. 3: changed title, and changed terminology throughout the paper, using "spectrahedral shadows" instead of "sdp representable sets". To appear in SIAGA