geometry-topology / Discrete geometry
How dense can a sphere packing in $\mathbb{R}^n$ be as $n \to \infty$? The Kabatiansky-Levenshtein upper bound stood for almost fifty years; the new proof improves the asymptotic upper bound all the way down to the Cohn-Elkies linear-programming threshold.
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upper bounds reach the Cohn-Elkies threshold; the true asymptotic density remains open
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How dense can a sphere packing in $\mathbb{R}^n$ be as $n \to \infty$? The Kabatiansky-Levenshtein upper bound stood for almost fifty years; the new proof improves the asymptotic upper bound all the way down to the Cohn-Elkies linear-programming threshold.
upper bounds reach the Cohn-Elkies threshold; the true asymptotic density remains open
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