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. Alex Koldobsky proposed a number of generalizations of this question to the case of the most general measures instead of the volume. Motivated by Koldobsky's work, we are studying a similar slicing problem when the volume functional is replaced by the lattice point enumerator (i.e. the number of integer lattice points inside a given set). This is a joint work with Matthew Alexander and Martin Henk. Speaker(s): Artem Zvavitch (Kent State University)