Leitung

Prof. Dr. Peter Bürgisser

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Technische Universität Berlin
Institut für Mathematik
Sekretariat MA 3-2
Straße des 17. Juni 136
10623 Berlin

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Raum MA 317 (3. OG)
Institut für Mathematik

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Beate Nießen
Raum MA 318
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No occurence obstructions in geometric complexity theory
Citation key	BIP - JAMS - No-Occurence-Obstructions-In-Geometric-Complexity-Theory
Author	Peter Bürgisser and Christian Ikenmeyer and Greta Panova
Pages	163–193
Year	2019
DOI	10.1090/jams/908
Journal	Journal of the American Mathematical Society
Volume	32
Number	1
Month	01
Abstract	The permanent versus determinant conjecture is a major problem in complexity theory that is equivalent to the separation of the complexity classes $VP_ws$ and $VNP$. Mulmuley and Sohoni [37] suggested to study a strengthened version of this conjecture over the complex numbers that amounts to separating the orbit closures of the determinant and padded permanent polynomials. In that paper it was also proposed to separate these orbit closures by exhibiting occurrence obstructions, which are irreducible representations of $GL(n^2, C)$, which occur in one coordinate ring of the orbit closure, but not in the other. We prove that this approach is impossible. However, we do not rule out the general approach to the permanent versus determinant problem via multiplicity obstructions as proposed in [37].