  The Ehrhart polynomial and Ehrhart series count lattice points in integer
dilations of a lattice polytope. We introduce and study a $q$-deformation of
the Ehrhart series, based on the notions of harmonic spaces and Macaulay's
inverse systems for coordinate rings of finite point configurations. We
conjecture that this $q$-Ehrhart series is a rational function, and introduce
and study a bigraded algebra whose Hilbert series matches the $q$-Ehrhart
series. Defining this algebra requires a new result on Macaulay inverse systems
for Minkowski sums of point configurations.
