Fourier Interpolation and Universal Optimality

In this talk I will describe recent joint work with Henry Cohn, Abhinav Kumar, Stephen D. Miller, and Danylo Radchenko. We study the problem of how to arrange points in euclidean space so as to minimize repulsion between them. We will show that this problem can be solved completely for a wide class of repulsive potentials in euclidean spaces of dimension 8 and 24. Moreover, an interesting byproduct of this project is a new type of Fourier interpolation formula.