Speaker
Description
Nonlocal interaction energies play a central role in describing the collective behaviour of large particle systems in a wide range of applications. In this lecture we will focus on interactions that are short-range repulsive and long-range attractive. We will review the key results on the existence and uniqueness of minimisers, and present their explicit characterisation in the classical case of isotropic kernels with Riesz-type repulsion and quadratic attraction. We will then show how a complete characterisation can be given for a broad class of anisotropic variants of the repulsive kernel. If time permits, we will conclude with a discussion of open problems and future directions. This talk is based on joint work with several collaborators: R. Frank, J. Mateu, L. Rondi, L. Scardia, E.G. Tolotti, and J. Verdera.