Mathematics of magic angles in a model of twisted bilayer graphene

Magic angles are a hot topic in condensed matter physics:when
two sheets of graphene are twisted by those angles the resulting
material is superconducting. I will present a very simple operator whose
spectral properties are thought to determine which angles are magical.It
comes from a recent PR Letter by Tarnopolsky--Kruchkov--Vishwanath. The
mathematics behind this is an elementary blend of representation
theory(of the Heisenberg group in characteristic three), Jacobi theta
functions and spectral instability of non-self-adjoint operators
(involving Hörmander's bracket condition in a very simple setting).
Spectral characterization of magic angles also allows precise numerical
computations and I will discuss the error bound issues arising there
(joint work with S Becker, Membree and J Wittsten).