I will introduce the main objects from spectral theory of

infinite dimensional operators: the domain, the resolvent and the

spectrum. I will then describe an analytic family of non normal operator

\(D(\alpha)\) (for \(\alpha \in \mathbb{C}\)) such that \(\alpha\mapsto\mathrm{Spec}(D(\alpha))\) is discontinuous. The points of discontinuity are called

"magic angles" and I will show that there are infinitely many of them.

This is joint work with Simon Becker and Maciej Zworski.

 

The existence of these angles were predicted by Bistritzer–MacDonald in

2011 and were observed experimentally in 2018. They correspond to

specific "twisting angles" between two sheets of graphene for which we

observe supraconductivity.