Abstract: Topological insulators (TI) are a class of 2D materials that behave like insulators in their bulk and conductors near the edge, which is mathematically characterized by the "emergence of edge spectrum". One of the key properties of TI is that the emergence of edge spectrum above is expected to be robust w.r.t. the shape of the edge. In this talk, we will discuss how the shape influences the emergence of edge spectrum. More explicitly, we will give a simple sufficient condition with a short, analysis proof; a counterexample with no emergence of edge spectrum when the condition fails; and further information about the edge spectrum in that case. This talk is based on a joint work with Alexis Drouot.

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