Ian Cavey

collaborators

7 papers

math.AG2026

Polytopes of Effective Boundary Expressions of Divisors on $M_{0, n}$

Ian Cavey, Deniz Genlik

For a divisor on $M_{0, n}$ , we introduce the polytope of its effective boundary expressions. We establish structural properties of these polytopes under the forgetful ma…

math.RT2026

A combinatorial rule for $G L$ -multiplicities of $A_{n}$ -quiver loci

Ian Cavey, Andrew Hardt, Alexander Yong

We give the first positive combinatorial rule for the multiplicities of irreducible $G L$ -representations in the coordinate rings of type $A$ quiver orbit closures, valid for every…

math.AG2026

Wall-crossing for Hilbert schemes

Ian Cavey, Eugene Gorsky, Alexei Oblomkov +1

The goal of the minimal model program for the Hilbert scheme of points on a surface aims is to describe the (stable) base loci of all divisors, their associated birational models,…

math.CO2026

Pattern expansions of permutation statistics

Ian Cavey, Hugh Dennin, Bridget Eileen Tenner

We study the expansions of permutation statistics in the basis of functions counting occurrences of a fixed pattern in a permutation. We show the finiteness of these pattern expans…

math.AG2025

Newton-Okounkov bodies for nested Hilbert schemes

Ian Cavey, Eugene Gorsky, Alexei Oblomkov +1

We study sections of line bundles on the nested Hilbert scheme of points on the affine plane. We describe the spaces of sections in terms of certain ideals introduced by Haiman, an…

math.CO2025

Graded Ehrhart theory and toric geometry