Recorded 21 May 2025. Didier Henrion of the Centre National de la Recherche Scientifique (CNRS) presents "Solving moment and polynomial optimization problems on Sobolev spaces" at IPAM's Statistical and Numerical Methods for Non-commutative Optimal Transport Workshop. Abstract: Using standard tools of harmonic analysis, we state and solve the problem of moments for non-negative measures supported on the unit ball of a Sobolev space of multivariate periodic trigonometric functions. We describe outer and inner semidefinite approximations of the cone of Sobolev moments. They are the basic components of an infinite-dimensional moment-sums of squares hierarchy, allowing to numerically solve non-convex polynomial optimization problems on infinite-dimensional Sobolev spaces with global convergence guarantees. Learn more online at: https://www.ipam.ucla.edu/programs/workshops/workshop-iii-statistical-and-numerical-methods-for-non-commutative-optimal-transport/