  We present and analyze a novel space-time hybridizable discontinuous Galerkin
(HDG) method for the linear free-surface problem on prismatic space-time
meshes. We consider a mixed formulation which immediately allows us to compute
the velocity of the fluid. In order to show well-posedness, our space-time HDG
formulation makes use of weighted inner products. We perform an a priori error
analysis in which the dependence on the time step and spatial mesh size is
explicit. We provide two numerical examples: one that verifies our analysis and
a wave maker simulation.
