Millikan 2099, Pomona College

The number of inversions of a permutation is an important statistic that arises in many contexts, including as the minimum number of simple transpositions needed to express the permutation and, equivalently, as the rank function for weak Bruhat order on the symmetric group. In this talk, I’ll describe an analogous statistic on the reduced expressions […]

Given an isotropic integral quadratic form which assumes a value t, we investigate the distribution of integer points at which this value is assumed. Building on the previous work about the distribution of small-height zeros of quadratic forms, we produce bounds on height of points outside of some algebraic sets in a quadratic space at […]