Explore a 50-minute lecture on adaptive sampling techniques for Delaunay triangulations of Riemannian manifolds. Delve into new quality bounds for point clouds that ensure successful manifold triangulation, particularly effective for manifolds with locally constant non-zero sectional curvature. Examine the method's approach of comparing the manifold to a constant curvature space using a map with small metric distortion. Analyze the impact of distortion on Voronoi and Delaunay decompositions, and understand the conditions for creating a correct triangulation of the manifold. Learn about the joint work of Hana Dal Poz Kouřimská and Mathijs Wintraecken, covering topics such as good point sampling, Voronoi diagrams, and the mapping process.