Rigidity of infinite-dimensional geometries

29.09.2026 10:30 – 11:30

This talk surveys recent research around the common theme of rigidity phenomena in non-linear infinite-dimensional geometries. Serving as our main protagonists are Ebin's space of Riemannian metrics on a closed manifold and the Wasserstein space of probability measures on a Riemannian manifold. Both are spaces of structures on a finite-dimensional base—a smooth manifold in the first case, and a Riemannian manifold in the second.

I will show that, despite being infinite-dimensional, these spaces do not gain new symmetries: every isometry essentially arises from symmetries of the base, with the single exception of the Wasserstein space over the real line. In fact, they remember exactly the structure they were fed: Ebin's space of metrics determines the smooth manifold up to diffeomorphism, and the Wasserstein space determines the underlying Riemannian manifold up to isometry.

Altogether, these findings suggest a broader paradigm for rigidity in such infinite-dimensional geometries. I will end with possible future directions, among them the Mabuchi metric of Kähler geometry and the behaviour at infinity of the Ebin space.

Lieu

Bâtiment: Conseil Général 7-9

Room 1-05, Tuesday 29.09.26, Séminaire "Groupes et géométrie"

entrée libre