Starting from a periodic system, one can by means of Bloch theory or discretisation form an effective geometry. In the standard case, this is a bundle over the Brillouin torus, whose sections are the states. More generally, one can consider families of Hamiltonians parameterized over a base. Such geometries can be thought of as classical or C* geometries. In the latter form, they appear via quiver representations. We will present the background and tools for the analysis of these geometries. This is joint work with R. Kaufmann and S. Khlebnikov
Effective geometries and their local and global invariants. Sponsored by the Meyer Fund
Effective geometries and their local and global invariants.