Ferromagnetism in the Hubbard model has been investigated for a long time.
Unfortunately, only few exact results are available. A class of models where
we were able to prove the existence and the uniqueness of ferromagnetic ground
states are the so called flat-band systems. They contain a flat band together
with several dispersive bands. Some of the results are valid for models with
a partially flat band. This is important progress, since it opens a way to