Applications of the Moment-SOS Hierarchy and the Christoffel Function

We would like to briefly describe new potential applications of the Moment-SOS hierarchy (e.g. in computational geometry, in solving some non linear PDE's, and some inverse problems in optimal control (with applications in Humanoid Robotics). Also I would like to introduce the Christoffel function (a well-known tool in approximation theory) which can have potential application in some data analysis problem (outlier detection, density estimation, dimension learning). It is simple tool, easy to use and with no optimization involved.