We will start by explaining how to associate a Newton polygon to an element in GL(n) over a field of Laurent series. This collection of Newton polygons forms a partially ordered set, and if we refine this construction by restricting to Newton polygons associated to elements in a fixed stratum of the affine Bruhat decomposition, there is a unique maximum element. The primary goal of this talk will be to provide a closed formula for computing this maximal element in terms of directed paths in the quantum Bruhat graph. Curiously, combining this result with work of Postnikov shows that our formula for the maximal Newton polygon coincides with that for the minimal monomial in the product of two Schubert classes in the quantum cohomology of the complete complex flag variety. Speaker(s): Elizabeth Milicevic (Haverford College)