Title: Equilibrium measures for nonlocal interaction energies: The role of anisotropy

Abstract: Particle systems subject to long-range interactions can be described, for large numbers of particles, in terms of continuum models involving nonlocal energies. For radially symmetric interactions, several authors have established qualitative properties of minimizers for this kind of energies. But what can be said for anisotropic interactions? Starting from an example that describes dislocation interactions in metals, I will discuss how the anisotropy may affect the optimal distribution of particles and, in particular, its dimensionality.