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General Mathematics Seminar of the St. Petersburg Division of Steklov Institute of Mathematics, Russian Academy of Sciences
June 23, 2022 13:00, St. Petersburg, POMI, room 311 (27 Fontanka). Also it is possible to watch this talk in Zoom, see https://logic.pdmi.ras.ru/GeneralSeminar/index.html


Dense sphere packings

M. A. Tsfasmanabc

a Institute for Information Transmission Problems of the Russian Academy of Sciences (Kharkevich Institute), Moscow
b Independent University of Moscow
c Institut de Mathématiques de Marseille (I2M, UMR 7373), Aix-Marseille Université–Centre National de la Recherche Scientifique



Abstract: How to place equal balls in the $N$-dimensional Euclidean space in the densest possible way? The problem is non-trivial even in dimension $N=2$. In dimension 3 the answer was obtained at the very end of 20th century, and for $N=4$ it is yet unknown.
In the introduction I shall present the history, the statement of the problem, and some well-known results. The main part is devoted to astounding results of Maryna Viazovska, who solved the problem in dimensions 8 and 24 using quasimodular forms. At the end I plan to recall some results of mine for very large dimensions $(N \to \infty)$, based on algebraic geometry and number theory.


© Steklov Math. Inst. of RAS, 2024