The APDE seminar on Monday, 4/8, will be given by Jens Wittsten (University of Borås) in-person in Evans 740, and will also be broadcasted online via Zoom from 4:10pm to 5:00pm PST. To participate, please email Federico Pasqualotto (fpasqualotto@berkeley.edu) or Mengxuan Yang (mxyang@math.berkeley.edu).

Title: Semiclassical quantization conditions for strained moiré lattices.

Abstract: When mechanical strain is applied to bilayer graphene in a certain way, an essentially one-dimensional moiré pattern can be seen. I will discuss a model for such systems and explain that it has approximately flat bands when the strain is very weak. The approximately flat bands correspond to approximate eigenvalues of infinite multiplicity, and they are obtained by generalizing the Bohr-Sommerfeld quantization condition for scalar symbols at a potential well to matrix-valued symbols with eigenvalues that coalesce precisely at the bottom of the well. The talk is based on joint work with Simon Becker.