8 sep 2021 -- 11:30   [open in google calendar]

Abstract.

Nonlocal energies are continuum models for large systems of interacting particles. They have countless applications, from biological systems to granular media, from vortices in superconductors to defects in metals.

A fundamental question in applications is the characterisation of minimisers of these energies; such minimisers correspond to ‘aggregation patterns’ and they are observed experimentally in biological systems and materials science.

In this talk I will discuss the `persistence' of the ellipse as energy minimiser, focusing on a class of perturbations of Coulomb energies.

This is based on ongoing work in collaboration with Joan Mateu, Maria Giovanna Mora, Luca Rondi and Joan Verdera.