Analysis seminar

Maciej Zworski: Magic Angles for Twisted Bilayer Graphene

Abstract: Magic angles refer to a remarkable theoretical (Bistritzer--MacDonald, 2011) and experimental (Jarillo-Herrero et al 2018) discovery, that two sheets of graphene twisted by a certain (magic) angle are a superconductor.

Mathematically, this is related to having a flat band of nontrivial topology for the corresponding periodic Hamiltonian which happens for a chiral model of twisted bilayer graphene (Tarnopolsky--Kruchkov--Vishwanath, 2019). I will report on mathematical analysis of these phenomena, with new contributions being a spectral characterization of magic angles, semiclassical analysis of the small angle limit, existence of infinitely many complex magic angles and description of multiplicities.

The talk is based on joint works with S Becker, M Embree, J Galkowski, M Hitrik, T Humbert and J Wittsten.