Algebra and Combinatorics Seminar

Date: March 24, 2023

Time: 3:00PM - 4:00PM

Location: BLOC 506A

Speaker: Avery St. Dizier , UIUC

Title: A Polytopal View of Schubert Polynomials

Abstract: Schubert polynomials are a family of multivariable polynomials whose product can be used to solve problems in enumerative geometry. Despite their many known combinatorial formulas, there remain mysteries surrounding these polynomials. I will describe Schubert (and the special case of Schur) polynomials with a focus on polytopes. From this perspective, I will address questions such as vanishing of Schubert coefficients, relative size of coefficients, and interesting properties of their support. Time permitting, I'll talk about my current work on generalizing the Gelfand–Tsetlin polytope, and its connections with representation theory and Bott–Samelson varieties.