Spectrahedral shadows
Claus Scheiderer

TL;DR
This paper demonstrates that many convex semi-algebraic sets in Euclidean space cannot be represented as spectrahedral shadows, providing a negative answer to a longstanding open question and disproving the Helton-Nie conjecture.
Contribution
The paper proves the non-existence of semidefinite representations for many convex semi-algebraic sets, refuting the Helton-Nie conjecture.
Findings
Many convex semi-algebraic sets lack semidefinite representations
Disproof of the Helton-Nie conjecture
Negative answer to Nemirovski's question
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.
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Taxonomy
TopicsMathematics and Applications · Digital Image Processing Techniques · Computational Geometry and Mesh Generation
