Fermiology in correlated electron systems

An overview is given for the way in which electron correlation effects such as magnetism or superconductivity are sensitively dominated by the band structure and the shape of the Fermi surface. This "fermiology in correlated electron systems" arises because the competition between various orders may take place on a subtle energy scale, and this concept can also be exploited in novel (or tailor-made) structures. Specifically we discuss (i) why and how the "flat-band" ferromagnetism can appear from the electron-electron repulsion, (ii) how superconductivity from the repulsion (with the fluctuation-exchange-mediated interaction) can be "optimised" with respect to the band structure. This includes an exotic possibility of spin-triplet pairing, or a recently proposed pairing on disconnected Fermi surfaces.