On integral well-rounded lattices

A lattice in R^n is called well-rounded, abbreviated WR, if it contains n linearly independent shortest vectors. Such lattices have many symmetries and play a central role in discrete optimization, extremal lattice theory, and related number theoretic problems. WR lattices corresponding to integral quadratic forms are of specific interest in the arithmetic context. In this talk, I will discuss some results on distribution properties of integral WR lattices, mostly concentrating on the planar case. In particular, I will present some counting estimates on the number of WR sublattices of planar lattices. If time allows, I will also talk about the special class of integral WR lattices, coming from ideals in number fields, giving a partial characterization of number fields for which such lattices exist.