H.B. Keller Colloquium

Monday, April 21, 2025

4:00pm to 5:00pm

Annenberg 105

Mathematics of magic angles in 2D structures

Maciej Zworski,, Professor of Mathematics, University of California, Berkeley,

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.

For more information, please contact Sumaia Abedin by phone at 6263956704 or by email at sabedin@caltech.edu or visit https://www.cms.caltech.edu/news-events/keller-colloquium.

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