I will give an introduction to the description of gapped free-fermion ground states in the Nambu space picture. This picture allows for a systematic description of all Altland-Zirnbauer symmetry classes in terms of so-called quasi-particle vacua with pseudo-symmetries. I will also explain a topological classification approach for gapped free-fermion ground states giving rise to a K-theoretic describtion of topological phases. This talk is based on joint work with A. Alldridge and M. Zirnbauer.
Fabien Vignes-Tourneret