Abstract: Optimal transport is a classical tool in pure and applied mathematics. With roots in geometry, it is a generalisation of the minimal matching problem and describes, loosely speaking, how to move sand from one area of land into another in the most cost effective way. In a broader context, it describes a resource allocation problem for which Leonid Kantorovich received the nobel price in economics, and it provides a natural way of measuring the distance between probability distributions (or histograms) which has widespread applications in statistics and machine learning. I will give a brief introduction to optimal transport and explain how it can be used as a tool in super resolution. In particular, I will present joint results with Michael Rawson were the resulting methods are applied to the problem of star cluster identification in astronomical imaging.
