Effective nonlinear models in many body problems.

We shall discuss how nonlinear models arise as effective theories in
many body physics, with main focus on nonlinear Schrödinger-type
equations. In particular, we will cover new applications in the theory
of ions immersed in Fermi gases, being a case of current experimental
relevance, and present a simple theorem about one intriguing difference
between the linear and non—linear case arising in dimension two.