Polynomials from Schubert calculus via diagrams

Polynomials are powerful tools in many fields, for example, representation theory, geometry, and topology. Understanding the combinatorics arising from polynomials may reveal important information in problems from these fields. This talk will focus on four polynomials from Schubert calculus: Schubert, key, Grothendieck, and Lascoux polynomials. I will discuss some combinatorial models related to these polynomials, including (K)-Kohnert diagrams and snow
diagrams. The K-Kohnert rule for Lascoux polynomial answers a conjecture by Ross and Yong, first stated in 2013. The combinatorial model of snow diagrams also provides a unified rule for computing the leading monomial of the top component of both Lascoux and Grothendieck polynomials, which has important algebraic and geometric interpretations. This talk is based on joint work with Tianyi Yu in arXiv 2206.08993 and 2302.03643.

Bio
https://sites.google.com/view/jianping-pan