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PL1: "Nonlocal interaction problems with anisotropy" Maria Giovanna Mora (U Pavia)
Time:
Monday, 18/Mar/2024:
3:00pm - 4:00pm
Session Chair: Sergio Conti
Location:G26/H1
Lecture Hall 1 in Building 26; size: 572
Presentations
Nonlocal interaction problems with anisotropy
M. G. Mora
Università di Pavia
Nonlocal interaction energies play a pivotal role in describing the behaviour of large systems of particles, in a variety of applications ranging from biology to physics and materials science. A fundamental question is understanding the optimal arrangement of particles at equilibrium, which are described, at least in average, by minimisers of the energy. Traditionally, the focus of the mathematical literature on nonlocal energies has been on radially symmetric potentials, which model interactions depending on the mutual distance between particles. On the other hand, the mathematical study of anisotropic potentials has been very limited until recently, despite their natural occurrence in modelling systems of particles where a preferred direction of interaction is present. In this lecture I will review some classical results for radially symmetric interactions and I will discuss some more recent results shedding light on the role of anisotropy on optimal distributions.
