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TU Berlin

Inhalt des Dokuments

Ehemalige Mitarbeiter

Dr. Christian Ikenmeyer

Lupe

Kontakt
University of Liverpool
Department of Computer Science
Ashton Building, Office 311
Ashton Street, Liverpool, L69 3BX
United Kingdom
 
Persönliche Homepage
http://pcwww.liv.ac.uk/~iken/

Publikationen in der Arbeitsgruppe

Explicit Lower Bounds via Geometric Complexity Theory
Zitatschlüssel BI-Explicit-Lower-Bounds-Via-Geometric-Complexity-Theory
Autor Peter Bürgisser and Christian Ikenmeyer
Buchtitel Proceedings 45th ACM Symposium on Theory of Computing
Seiten 141-150
Jahr 2013
Zusammenfassung We prove the lower bound $R(M_m) \ge \frac32 m^2 - 2$ on the border rank of $m × m$ matrix multiplication by exhibiting explicit representation theoretic (occurence) obstructions in the sense of Mulmuley and Sohoni's geometric complexity theory (GCT) program. While this bound is weaker than the one recently obtained by Landsberg and Ottaviani, these are the first significant lower bounds obtained within the GCT program. Behind the proof is the new combinatorial concept of obstruction designs, which encode highest weight vectors in $\mathrmSym^d \bigotimes^3(\mathbb C^n)^*$ and provide new insights into Kronecker coefficients.
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