Ian Cavey

activity

20222026

collaborators

10 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

Ian Cavey

We give two new constructions of the harmonic algebra of a lattice polytope $P$ , a bigraded algebra whose character is the $q$ -Ehrhart series of $P$ defined by Reiner and Rhoades.…

math.CO2025

Domino Tilings, Domino Shuffling, and the Nabla Operator

Ian Cavey, Yi-Lin Lee

We study domino tilings of certain regions $R_{λ}$ , indexed by partitions $λ$ , weighted according to generalized area and dinv statistics. These statistics arise from the $q, t$ -Catal…

math.AG2024

Verlinde series for Hirzebruch surfaces

Ian Cavey

We give an explicit formula for Euler characteristics of line bundles on the Hilbert scheme of points on $P^{1} \times P^{1}$ . Combined with structural results of Ellin…

math.CO2022

q,t-Catalan measures

Ian Cavey

We introduce the $q, t$ -Catalan measures, a sequence of piece-wise polynomial measures on $R^{2}$ . These measures are defined in terms of suitable area, dinv, and bounce stat…

math.AG2022

Effective divisors and Newton-Okounkov bodies of Hilbert schemes of points on toric surfaces

Ian Cavey

We compute the (unbounded) Newton-Okounkov body of the Hilbert scheme of points on $C^{2}$ . We obtain an upper bound for the Newton-Okounkov body of the Hilbert scheme of poi…

Polytopes of Effective Boundary Expressions of Divisors on M0,n​

A combinatorial rule for GL-multiplicities of An​-quiver loci

Wall-crossing for Hilbert schemes

Pattern expansions of permutation statistics

Newton-Okounkov bodies for nested Hilbert schemes

Graded Ehrhart theory and toric geometry

Domino Tilings, Domino Shuffling, and the Nabla Operator

Verlinde series for Hirzebruch surfaces

q,t-Catalan measures

Effective divisors and Newton-Okounkov bodies of Hilbert schemes of points on toric surfaces

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

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