Thinking outside the box: spherical geometry in chemistry and physics

Spherical models offer unparalleled mathematical simplicity. They have been extensively used in chemistry and physics to develop a variety of simple approximations that, despite their simplicity, contain the key physics of more complicated systems, and are accurate enough to have chemical and physical usefulness. In this proposal, I will take advantage of the superiority of the spherical geometry to tackle some fundamental unsolved problems, such as the spontaneous broken-symmetry states of the uniform electron gas, the physics of many-electron quantum rings and exciton-like quasiparticles, and the relativistic behaviour of the many-electron wave function. Each of these objectives will lead to new insights in their field.