The Castelnuovo-Mumford Regularity of Matrix Schubert Varieties

Abstract: The Castelnuovo-Mumford regularity of a graded module provides a measure of how complicated its minimal free resolution is. In work with Rajchgot, Ren, Robichaux, and St. Dizier, we noted that the regularity of Matrix Schubert Varieties can be easily obtained by knowing the degree of the corresponding Grothendieck polynomial. Furthermore, we gave explicit, combinatorial formulas for the degrees of symmetric Grothendieck polynomials. In this talk, I will present a combinatorial degree formula for arbitrary Grothendieck polynomials. This is joint work with Oliver Pechenik and David Speyer.

combinatoricscategory theoryrepresentation theory

Audience: researchers in the topic

( slides )

The TRAC Seminar - Théorie de Représentations et ses Applications et Connections