Hypertoric geometry and Gromov-Witten theory

We study Gromov-Witten theory of hypertoric Deligne-Mumford stacks from two points of view. From the viewpoint of representation theory, we calculate the operator of small quantum product by a divisor, following \cite{BMO}, \cite{MO}, \cite{MS}. From the viewpoint of Lawrence toric geometry, we compare Gromov-Witten invariants of a hypertoric Deligne-Mumford stack with those of its associated Lawrence toric stack.