Closure of bulk spectral gap for topological insulators with general edges

Topological insulators are materials that exhibit unique physical properties due to their non-trivial topological order. One of the most notable consequences of this order is the presence of protected edge states as well as closure of bulk spectral gaps, which is known as the bulk-edge correspondence.

In this talk, I will discuss the mathematical description of topological insulators and their related spectral properties. The presentation will begin with an overview of Floquet theory, Bloch bundles, and the Chern number. We will then examine the bulk-edge
correspondence in topological insulators before delving into our research on closure of bulk spectral gaps for topological insulators with general edges. This talk is based on a joint work with Alexis Drouot.