On the linear span of lattice points in a parallelepiped

ACO Student Seminar
Friday, November 13, 2015 - 13:05
1 hour (actually 50 minutes)
Skiles 005
Georgia Tech
We find a good characterization for the following problem: Given a rational row vector c and a lattice L in R^n which contains the integer lattice Z^n, do all lattice points of L in the half-open unit cube [0,1)^n lie on the hyperplane {x in R^n : cx = 0}? This work generalizes a theorem due to G. K. White, which provides sufficient and necessary conditions for a tetrahedron in R^3 with integral vertices to have no other integral points. Our approach is based on a novel proof of White's result using number-theoretic techniques due to Morrison and Stevens. In this talk, we illustrate some of the ideas and describe some applications of this problem.