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math.MG2016
A Reverse Minkowski Theorem
Oded Regev, Noah Stephens-Davidowitz
$ \newcommand{\R}{\mathbb{R}} \newcommand{\lat}{\mathcal{L}} $We prove a conjecture due to Dadush, showing that if $\lat \subset \R^n$ is a lattice such that $\det(\lat') \ge 1$ fo…
math.MG2016★ 2 cited
A Note on Koldobsky's Lattice Slicing Inequality
Oded Regev
$ \newcommand{\R}{\mathbb{R}} \newcommand{\Z}{\mathbb{Z}} \renewcommand{\vec}[1]{\mathbf{#1}} $We show that if is an origin-symmetric convex body, then there exist…
math.MG2016
Towards Strong Reverse Minkowski-type Inequalities for Lattices
Daniel Dadush, Oded Regev
We present a natural reverse Minkowski-type inequality for lattices, which gives upper bounds on the number of lattice points in a Euclidean ball in terms of sublattice determinant…