Symmetries of Wasserstein spaces

Abstract: Let $\mathbb{P}_p(X)$ be the space of probability measures with finite $p-$moments on a metric space $(X,d).$ Using solutions to the optimal transport problem of Monge-Kantorovich it is possible to equip $\mathbb{P}_p(X)$ with a distance $\mathbb{W}_p$ known as the $L^p-$Wasserstein distance.

With this the resulting metric space $(\mathbb{P}_p(X), \mathbb{W}_p)$ will share many geometrical properties with the base space $(X,d)$ such as: compactness, existence of geodesics, and even non-negative sectional curvature bounds (when $p=2$).

Therefore, a natural question is whether it is possible for $(\mathbb{P}_p(X), \mathbb{W}_p)$ to be more symmetric than the original space $(X,d).$ In this talk we will first introduce the optimal transport problem, Wasserstein spaces, and some of its properties. Once this is done we will discuss some of the results regarding isometries in these spaces.

differential geometrygeometric topologymetric geometry

Audience: researchers in the topic

( video )

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Virtual seminar on geometry with symmetries

Series comments: Description: Research seminar in Lie group actions in Differential geometry.

The seminar meets every other Wednesday. To accommodate most time zones, the time rotates. The Zoom link is sent to the mailing list around 24 hours before each talk. To subscribe to the mailing list, fill the following form: docs.google.com/forms/d/e/1FAIpQLSdKrJ-nivgjr7ZVJmIY0qkN-VbzTl5NHHNyg6nNsCqjhB-4WA/viewform?usp=sf_link.

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