Refereed Contributions

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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