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UID:node-3091533@mathematics.huji.ac.il
DTSTAMP:20220524T110000Z
DTSTART:20220524T110000Z
DTEND:20220524T120000Z
SUMMARY:Dynamics seminar: Or Ordentlich (HUJI) Bounds on the density of nearly uniform lattice coverings
DESCRIPTION:*Abstract:*The \eps-smooth covering density of a unit co-volume lattice L \nwith respect to a convex body K is defined as the minimum volume of a dilate \nrK such that each point x\in R^n is rK-covered by (1\pm \eps)\Vol(r K) points \nin L. For any convex body K in R^n we show that for almost all lattices (with \nrespect to the natural Haar-Siegel\nmeasure on the space of lattices) the \eps-smooth covering density is \npolynomial in n. We also show similar results for random construction A \nlattices, provided that the ratio between the covering and packing radii of \nZ^n with respect to K is at most polynomial in n.Our proofsutilize a recent \nbreakthrough of Dhar and Dvir on the discrete Kakeya problem.\nJoint work with Oded Regev and Barak Weiss\n*\nZoom details (Ordentlich)*\nJoin Zoom Meeting [1]\nMeeting ID: 858 4735 8933\nPasscode: 210976\n\n[1] https://huji.zoom.us/j/85847358933?pwd=TUQ1T1pDQlErakZmUHFRWElEeE9Ldz09\n
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