Jan Rolfes: The covering number in different settings

Abstract: The covering number is a fundamental concept in metric geometry. For a compact metric space (X,d) and a given radius r, it asks for the minimal number of r-balls needed to cover the space X. In this talk, I focus on specific examples of metric spaces in the areas of geometry, probability theory and quantum computing. In particular, we discuss how recent approximation methods, inspired by moment methods in polynomial optimization, can be applied to these spaces.