H.B. Keller Colloquium
Maciej Zworski, FRSC, is a Professor of Mathematics at the University of California, Berkeley. His research lies at the intersection of microlocal analysis, scattering theory, and partial differential equations, with significant contributions to each of these fields. He was an invited speaker at the International Congress of Mathematicians held in Beijing in 2002 and delivered a plenary lecture at the Dynamics, Equations and Applications conference in Kraków in 2019.
Magic angles refer to a remarkable theoretical (Bistritzer--MacDonald, 2011) and experimental (Cao et al 2018) discovery, that two sheets of graphene twisted by certain (magic) angles display unusual electronic properties such as superconductivity.
Mathematically, this is related to having flat bands of nontrivial topology for the corresponding periodic Hamiltonian and their existence was shown in the chiral model of twisted bilayer graphene (Tarnopolsky-Kruchkov-Vishwanath, 2019). A spectral characterization of magic angles (Becker--Embree--Wittsten--Z, 2021, Galkowski--Z, 2023) also produces complex values and the distribution of their reciprocals looks remarkably like a distribution of scattering or Pollicott--Ruelle resonances, with the real magic angles corresponding to anti-bound states. I will provide a gentle introduction to the subject and highlight some recent results.
The talk is based on joint works with S Becker, M Embree, J Galkowski, M Hitrik, T Humbert, Z Tao, J Wittsten and H Zeng.