University of Minnesota Combinatorics Seminar: 2022

Date: 01/01/2022

Speaker: Avery St Dizier

A Polytopal View of Schubert Polynomials
Schubert polynomials are distinguished 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 the special case of Schur) 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. Time permitting, I will discuss some recent work on Grothendieck polynomials, K-theory analogues of Schubert polynomials.

A Polytopal View of Schubert Polynomials

Schubert polynomials are distinguished 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 the special case of Schur) 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. Time permitting, I will discuss some recent work on Grothendieck polynomials, K-theory analogues of Schubert polynomials.