Thesis title: A variational approach to nonlocal interactions: discrete-to-continuum analysis, ground states and geometric evolutions
This thesis deals with variational models for systems governed by nonlocal interactions. In
particular, we analyze systems of hard spheres governed by attractive Riesz potentials, surface
energies related to fractional perimeters and gradient flows of such energies leading to local and
nonlocal geometric evolutions; eventually, we consider similar problems for densities governed
by Gagliardo-type seminorms, focussing on fractional heat flows.