Points on manifolds: covering, Monte Carlo type integration, and approximation

Abstract: 

Selecting suitable nodes on the real line, the unit interval, and the unit sphere for integration and interpolation purposes have a long tradition in numerical mathematics. In fact, deeper studies of the interval and the sphere are still an active field of research. We shall discuss some recent extensions to more general compact manifolds. Our perspective is focused on connecting theoretical results with numerical experiments. We shall always be guided by the Grassmannian manifolds, for which the projective space is a particular example and closely relates to the unit sphere.