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 Braverman, Maulik and Okounkov (2011) and McBreen and Shenfeld (2013). From the viewpoint of Lawrence toric geometry, we compare the Gromov-Witten invariants of a hypertoric Deligne-Mumford stack with those of its associated Lawrence toric Deligne-Mumford stack.