Spring 2020

New Bounds on the Covering Density

Tuesday, Feb. 18, 2020 3:30 pm4:15 pm PST

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Barak Weiss, Tel Aviv University


Calvin Lab Auditorium

We obtain new upper bounds on the minimal density of lattice coverings of R^n by dilates of a convex body K. We also obtain bounds on the probability (with respect to the natural Haar-Siegel measure on the space of lattices) that a randomly chosen lattice L satisfies L+K=R^n. As a step in the proof, we utilize and strengthen results on the discrete Kakeya problem. Joint work with Or Ordentlich and Oded Regev.