Rui Xiong (part 2): "Chern Schwartz-MacPherson Classes on Flag Varieties: Pieri Rules, Conjectures"
Channel: Schubert Seminar
Date: 2023-05-08

Abstract: In this talk, we will present our recent work on Chern-Schwartz-MacPherson (CSM) classes over classical flag varieties. We will begin by providing a concise introduction to CSM classes and their properties. Our main contribution is the derivation of an equivariant CSM Pieri rule, which generalizes and unifies many known formulas for CSM classes and Schubert classes. We will also discuss some related conjectures on CSM classes, and their implications in algebraic geometry. Lastly, we will highlight an application of the Murnaghan-Nakayama rule to the enumeration of domino tableaux, an area of combinatorics that has connections to representation theory. Our results are obtained jointly with Neil J.Y. Fan and Peter L. Guo.