Title: A measure of maximal entropy for geodesic flows of nonstrictly convex Hilbert geometries
Speaker: Harrison Bray (University of Michigan)
Abstract: Strictly convex Hilbert geometries naturally generalize constant negatively curved Riemannian geometries, and the geodesic flow on quotients 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 a geometric approach to studying the geodesic flow in this setting, culminating in a measure of maximal entropy which is ergodic for the geodesic flow.