Mathematical results on the chiral model of twisted bilayer graphene (with an appendix by Mengxuan Yang and Zhongkai Tao)

The study of twisted bilayer graphene (TBG) is a hot topic in condensed matter physics with special focus on {\em magic angles} of twisting at which TBG acquires unusual properties. Mathematically, topologically non-trivial flat bands appear at those special angles. The chiral model of TBG pioneered by Tarnopolsky–Kruchkov–Vishwanath has particularly nice mathematical properties and we survey, and in some cases, clarify, recent rigorous results which exploit them.