Analysis Seminar

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Optimal transport metrics on fiber bundles by disintegration

Speaker: Jun Kitagawa, Michigan State University

Location: Warren Weaver Hall 1302

Date: Tuesday, November 26, 2024, 3:45 p.m.

Synopsis:

I will discuss a new family of metrics (which we call the Disintegrated Monge-Kantorovich metrics) on probability measures on a metric fiber bundle with fixed base marginal, and the geometric structure induced by this family. The disintegrated Monge-Kantorovich metrics include the linearized optimal transport metric, and certain cases also admit an isometric embedding of the sliced Wasserstein metrics. I will also talk about barycenter problems utilizing this new family of metrics; as one corollary of our results we obtain uniqueness of classical Wasserstein barycenters on any connected Riemannian manifold (with no condition on curvatures, injectivity radius, or boundary) when one of the marginal measures is absolutely continuous. This talk is based on joint work with Asuka Takatsu (Tokyo Metropolitan University).

Notes:

Special Analysis Seminar.