Strictly convex Hilbert geometries naturally generalize constant negatively curved Riemannian geometries, and the geodesic flow on quotient manifolds has been well-studied by Benoist, Crampon, Marquis, and others. In contrast, nonstrictly convex Hilbert geometries in three dimensions have the feel of nonpositive curvature, but also have a fascinating geometric irregularity which forces the geodesic flow to avoid direct application of existing nonuniformly hyperbolic theory. In this talk, we present our approach to studying the geodesic flow in this setting, culminating in a measure of maximal entropy which is ergodic for the geodesic flow. Speaker(s): Sarah Bray (UM)