Wasserstein Spaces: Geometry & Applications

Topic: Wasserstein Spaces: Geometry & Applications

Emergent Mind: https://www.emergentmind.com/articles/wasserstein-spaces
Sign up for our free trending papers email digest: https://www.emergentmind.com/subscribe
Follow us on X: https://x.com/EmergentMind
Join our Discord: https://discord.gg/BhfTC4mTXq

This lightning talk introduces Wasserstein spaces, metric spaces of probability measures equipped with optimal transport distances. We explore their rich geometric structure—from geodesics and curvature to isometry rigidity and flexibility—revealing how the geometry of the underlying space shapes the infinite-dimensional Wasserstein geometry. We examine key properties including Riemannian-like structure, dimension theory, and stability results, and highlight applications spanning statistics, PDEs, and data science.

Видео Wasserstein Spaces: Geometry & Applications канала Emergent Mind