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Sphere packings and automorphic forms A. B. Kalmynin International laboratory for Mirror Symmetry and Automorphic Forms, National Research University "Higher School of Economics" (HSE), Moscow |
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Abstract: The densest sphere packing problem is a multi-dimensional generalization of the famous Kepler conjecture. In 2016 M. Vyazovskaya was able to completely solve the problem in dimensions 8 and 24, where densest packings correspond to E_8 lattice and Leech lattice respectively. We will discuss the proof of Vyazovskaya's result, which surprisingly uses certain properties of automorphic forms. |
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