Seminar
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| Location: | SLMath: Eisenbud Auditorium, Online/Virtual |
Keywords and Mathematics Subject Classification (MSC)
Primary Mathematics Subject Classification
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Lattice packing of spheres in high dimensions using a stochastically evolving ellipsoid
I will present a recent result of Klartag that there exists a lattice sphere packing in R^n with density at least cn^2 2^{-n}. This is equivalent to the existence of an origin-symmetric ellipsoid in R^n of volume cn^2 that contains no lattice point other than the origin. The proof involves stochastically evolving an ellipsoid until it touches cn^2 lattice points on its boundary. I will discuss the details of this stochastic process, and the methods used to analyze it.
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