# Emergent Topology From Finite Volume Topological Insulators

# Emergent Topology From Finite Volume Topological Insulators

**In-Person Talk **

Finite volume (or area) models for topological insulators are closer to experiment than innite volume models. However they are only indirectly connected to Brillouin zone and so we need to look elsewhere for a topological space. Fortunately, for three or more noncommuting hermitian matrices, there is an associated joint spectrum that can be a rich topological space. Utilizing the K-theory of such a space we can quantify the stability of bound states in nite models and predict the instability caused by disorder and defect. Joint spectrum stabilized by K-theory applies to topological insulators in many symmetry classes and many dimensions and even arises in the study of D-branes. This talk, however, will focus on Chern insulators, especially those based on a quasicrystal. In this case it seems that it is only possible to deduce the index of the relevant Fredholm operator using computer calculations on nite models.