Uniqueness of the measure of maximal entropy for geodesic flows of surfaces with caps

The class of surfaces in this talk was introduced in the 1980s by Donnay in order to exhibit a smooth Riemannian metric on the two sphere with ergodic geodesic flow. The geodesic flows for these surfaces have unique (and therefore ergodic) measures of maximal entropy. The proof uses Climenhaga and Thompson's extension of the approach pioneered by Bowen and Franco. This is joint work with Todd Fisher and Rachel McEnroe.