On the degree, size, and chromatic index of a uniform hypergraph
Journal of Combinatorial Theory Series A
Geometric Complexity Theory I: An Approach to the P vs. NP and Related Problems
SIAM Journal on Computing
Completeness classes in algebra
STOC '79 Proceedings of the eleventh annual ACM symposium on Theory of computing
Geometric Complexity Theory II: Towards Explicit Obstructions for Embeddings among Class Varieties
SIAM Journal on Computing
On P vs. NP and geometric complexity theory: Dedicated to Sri Ramakrishna
Journal of the ACM (JACM)
The Conjectures of Alon-Tarsi and Rota in Dimension Prime Minus One
SIAM Journal on Discrete Mathematics
Algebraic Complexity Theory
Geometric complexity theory and tensor rank
Proceedings of the forty-third annual ACM symposium on Theory of computing
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We prove the lower bound R Mm) ≥ 3/2 m2-2 on the border rank of m x 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 an explicit description of the highest weight vectors in Symd⊗3 (Cn)* in terms of combinatorial objects, called obstruction designs. This description results from analyzing the process of polarization and Schur-Weyl duality.