General Events - Department of Mathematics

Schubert polynomials are polynomial representatives of cohomology classes of subvarieties of the flag manifold. Despite the many combinatorial formulas developed for them over the years, there remain many mysteries surrounding these polynomials.

I will describe Schubert (and related) polynomials with a focus on discrete geometry. From this perspective, I will address questions such as vanishing of Schubert coefficients, relative size of coefficients, and interesting properties of the support of a Schubert polynomial. I will discuss some extensions to Grothendieck polynomials, K-theory analogues of Schubert polynomials.