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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 , a bigraded algebra whose character is the -Ehrhart series of 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 , indexed by partitions , weighted according to generalized area and dinv statistics. These statistics arise from the -Catal…