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Multiplying matrices via polynomials: exposition and barriers
We give an exposition of OpenAI's recent proof that the exponent $ω_\mathbb{C}$ of matrix multiplication over the complex numbers satisfies $ω_\mathbb{C}\leq9/4$. Our version of the proof gives $ω_\mathbb{F}\leq9/4$ over every field $\mathbb{F}$. We also treat the rectangular matrix multiplication e
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