In their study of infinite flag varieties, Lam, Lee, and Shimozono (2021) introduced bumpless
pipe dreams in a new combinatorial formula for double Schubert polynomials. These …

Knutson and Miller (2005) established a connection between the anti-diagonal Gr\" obner
degenerations of matrix Schubert varieties and the pre-existing combinatorics of pipe …

The geometric vertex decomposability property for polynomial ideals is an ideal-theoretic
generalization of the vertex decomposability property for simplicial complexes. Indeed, a …

We initiate a study of the Gröbner geometry of local defining ideals of Hessenberg varieties
by studying the special case of regular nilpotent Hessenberg varieties in Lie type A, and …

Schubert patch ideals are a class of generalized determinantal ideals. They are prime
defining ideals of open patches of Schubert varieties in the type A flag variety. In this paper …

A major open question in the theory of Gorenstein liaison is whether or not every
arithmetically Cohen-Macaulay subscheme of $\mathbb {P}^ n $ can be G-linked to a …

We study three invariants of geometrically vertex decomposable ideals: the Castelnuovo-
Mumford regularity, the multiplicity, and the $ a $-invariant. We show that these invariants …

A regular nilpotent Hessenberg Schubert cell is the intersection of a regular nilpotent
Hessenberg variety with a Schubert cell. In this paper, we describe a set of minimal …

Over the course of more than 150 years a beautiful theory of liaison has emerged.
Classically, complete intersections were used for the links. A systematic study of liaison …

Grobner bases are an important tool for working with ideals in polynomial rings. They have
both computational and theoretical importance. In this dissertation, we produce Grobner …