The talk is devoted to measures and point configurations optimizing energies based on multivariate potentials. The emphasis is put on potentials defined by geometric characteristics of point subsets and multivariate versions of classical two-point potentials such as Riesz potentials or p-frame potentials. As the main machinery, we adapt the semidefinite programming method to this context.
This research is a part of the joint project with Dmitriy Bilyk, Damir Ferizovic, Ryan Matzke, Josiah Park, Oleksandr Vlasiuk.