Georgia Institute of Technology College of Sciences

In this talk I will describe those linear subspaces of $\mathbf{R}^d$ which can be formed by taking the linear span of lattice points in a half-open parallelepiped. I will draw some connections between this problem and Keith Ball's cube slicing theorem, which states that the volume of any slice of the unit cube $[0,1]^d$ by a codimension-$k$ subspace is at most $2^{k/2}$.