Abstract: The quadratic Wasserstein space over a Riemannian manifold inherits asurprisingly rich geometry from its base. In this talk, I will address the question of geometric rigidity for these spaces. The main result establishes that the isometries of the Wasserstein space are entirely induced by the isometries of the Riemannian base if and only if the base lacks a Euclidean de Rham factor. In addition, the Wasserstein space determines the underlying manifold up to isometry. I will outline the main ideas for the proof of this characterization and place it into a wider context by surveying foundational developments in the geometry of Wasserstein spaces from the last two decades.
Bei Interesse an einer online-Teilnahme (sei es regelmäßig oder auch nur an einem bestimmten Vortrag) bitten wir vorab mit Tobias Weich Kontakt aufzunehmen, damit der Teilnahmelink geteilt werden kann.