Wasserstein Geometry, the Otto Metric, and Divergences

How do we measure the distance between two probability distributions? While classical approaches often treat distributions as static functions, the theory of Optimal Transport offers a dynamic perspective: the distance reflects the minimal effort required to rearrange one distribution into another. This geometric viewpoint transforms the space of probability measures into an infinite-dimensional Riemannian manifold - an idea formalized by the Otto calculus. In this talk, we will explore the rich geometry of this "Wasserstein space" and relate it to other classical notions of Information Geometry.