Alexey Glazyrin (University of Texas Rio Grande Valley)「Optimal point configurations and measures for multivariate potentials on spheres」
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 such as volumes and areas. As the main machinery, we adapt the semidefinite programming method to this context. Interestingly, this machinery also provides a new proof of a classical problem of Erdős about nearly orthogonal sets that can be interpreted as a three-point packing problem.