Barak Weiss: New bounds on the covering density of lattices

Abstract: 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.