the successive minima of an order in a degree n number field are n real numbers encoding information about the euclidean structure of the order. how many orders in degree n number fields are there with almost prescribed successive minima, fixed galois group, and bounded discriminant? in this talk, i will address this question for n = 3, 4, 5. the answers, appropriately interpreted, turn out to be piecewise linear functions on certain convex bodies. if time permits, i will also discuss function field analogues of this problem.

[pre-talk at 1:20pm]