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Durham University

Research & business

Research lectures, seminars and events

The events listed in this area are research seminars, workshops and lectures hosted by Durham University departments and research institutes. If you are not a member of the University, but  wish to enquire about attending one of the events please contact the organiser or host department.


 

Geometry and Topology Seminar: Rigidity of Wasserstein isometries in closed Riemannian manifolds

Presented by Jaime Santos, Universidad Autónoma de Madrid
22 October 2020 13:00 in CM301

Let P2(M) be the space of probability measures on a Riemannian manifold M. Using the solutions to Monge-Kantorovich’s optimal transport problem it is
possible to define a distance on P2(M), the so called L2−Wasserstein distance W2. This distance reflects many geometrical properties of the manifold such as: compactness, geodesics, and non-negative sectional curvature.
In this talk we will discuss some intrinsic properties of Wasserstein spaces, more precisely we give a positive answer to the following question:
If two closed Riemannian manifolds M, N are such that their corresponding Wasserstein spaces P2(M), P2(N) are isometric, does it follow then that M is isometric to N?
Moreover, if we assume that the Riemannian manifold has positive sectional curvature we can also prove that the isometry groups of the manifold M and of the
Wasserstein space P2(M) coincide.

Contact F. Galaz-Garcia for more information