Martin Henk: Discrete Slicing Problem

Abstract

The well-known (and still open) slicing problem in Convex Geometry
asks whether there exists an absolute constant $c$ so that for every
origin-symmetric convex body $K$  of volume 1 there is a hyperplane
section of $K$ whose $(n − 1)$-dimensional volume is greater than $c$.
Motivated by a question of Alexander Koldobsky, we are studying
a similar  slicing problem (as well as related problems)
when the volume functional is replaced by the lattice point enumerator.

(Based on joint works with Matthew  Alexander, Sören Berg and Artem Zvavitch.)