Conjugate points in Wasserstein space

The student studies critical points of the exponential map on Wasserstein space of probability measures on a Riemannian manifold. The questions that are addressed are whether they are isolated along a given geodesic in general or only for a certain class of underlying Riemannian manifolds. More generally, the student studies the global analysis and geometry of this metric space and properties that generalize to Hadamard spaces.