Symmetry in Equivariant Schubert Calculus of $\mathbb{P}^n$

Time: 16:30, August 19, 2026

Venue: Room 612, Building A6

Online Zoom link:  https://zoom.us/j/99636681387?pwd=0WscBnehOJig68SqctGluVuA3RwraE.1

Abstract: How many lines in $\mathbb{P}^3$ meet four general lines? This classical problem illustrates Schubert's symbolic calculus, whose rigorous foundation was the
subject of Hilbert's fifteenth problem. Modern Schubert calculus interprets such enumerative questions as intersection products on Grassmannians, with
connections to Schur functions, Littlewood-Richardson coefficients, and representation theory.

We then turn to the $T$-equivariant cohomology of $\mathbb{P}^n$. Anderson and Fulton asked for a combinatorial formula for its structure coefficients that makes
positivity and symmetry manifest. We present such a formula using weighted matchings on bipartite graphs. The model also yields refined saturation results
for the monomial supports of these coefficients.