Mathematics of magic angles

Speaker:Dr. Simon Becker (ETH Zurich)
Schedule:Fri., 16:00-17:00, Sept. 8, 2023
Venue:Lecture Hall C548, Tsinghua University Shuangqing Complex Building A(清华大学双清综合楼A座C548报告厅); Zoom Meeting ID: 271 534 5558 Passcode: YMSC


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 2019 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). Recent mathematical progress also includes the proof of existence of generalized magic angles and computer assisted proofs of existence of real ones (Luskin--Watson, 2021).
The results will be illustrated by colourful numerics which suggest many open problems (joint work with M Embree, J Wittsten, and M Zworski in 2020 and T Humbert and M Zworski in 2022-23).


Dr. Becker is currently an Hermann-Weyl Instructor in ETH Zurich. He graduated from Cambridge (PhD) in 2021 and worked for one year in NYU as Courant Instructor.