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SUMMARY:WKB structure in a scalar model of flat bands - Maciej Zworski (
 University of California\, Berkeley)
DTSTART:20260302T140000Z
DTEND:20260302T150000Z
UID:TALK242149@talks.cam.ac.uk
CONTACT:Zoe Wyatt
DESCRIPTION:The scalar model of flat bands is a simplification of models i
 n condensed matter physics. It allows the study of relevant spectral probl
 ems using a 2nd order scalar equation\, akin to the Schroedinger equation 
 with the square of dbar on a torus replacing the Laplacian. It displays ma
 ny features of original models such as the ``quantisation" of the reciproc
 als of magic angles at which flat bands appear. The space of solutions can
  be described using a rank 2 holomorphic vector bundle over the torus and 
 its properties as alpha varies are related to the structure of bands leadi
 ng to a trichotomy: tangential touching (most of alphas)\, Dirac points (d
 iscrete set of\nalphas) and flat bands (discrete set). (Mengxuan Yang and 
 Bryan Li observed that the same argument works in a more physically realis
 tic setting of twisted two-layered wafers of graphene.)\n\nIn my talk I wi
 ll describe the basic properties of the scalar model and of the general cl
 ass of scalar equations to which it belongs. I will also present a discuss
 ion of WKB-like structure of solutions.\n\nThis is joint work with S Dyatl
 ov and H Zeng\, with earlier contributions by S Becker\, M Embree\, J Galk
 owski\, M Hitrik\, T Humbert\, Z Tao\, J Wittsten and M Yang.
LOCATION:MR13
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