OR + DM Seminar: Imre Bárány

It is well known that a line can intersect at most 2n-1 cells of the n x n chessboard. What happens in higher dimensions: how many cells of the d-dimensional [0,n]^d box can a hyperplane intersect? We also prove the integer analogue of the following fact. If K, L are convex bodies in R^d and $K\subset L$, then the surface area K is smaller than that of L.

Joint work with Peter Frankl.