On discrete subgroups of Euclidean spaces (Lenny Fukshansky, CMC)

Let x_1,…,x_n be an overdetermined spanning set for the Euclidean space R^k, where n > k. Let L be the integer span of these vectors. Then L is an additive subgroup of R^n. When is it discrete in R^n? Naturally, this depends on the choice of the spanning set, but in which way? We will review some classical results leading up to this question and then will discuss some more recent developments.