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SUMMARY:The curious spectra and dynamics of non-locally finite crystals - 
 Matthias Täufer (University Polytechnic Hauts-De-France)
DTSTART:20260302T143000Z
DTEND:20260302T153000Z
UID:TALK242065@talks.cam.ac.uk
DESCRIPTION:We investigate the spectral theory of periodic graphs which ar
 e not locally finite but carry non-negative\, symmetric and summable edge 
 weights. These periodic graphs are shown to have rather intriguing behavio
 ur. We shall discover &ldquo\;partly flat bands&rdquo\; which are only fla
 t for certain quasimomenta. We construct a periodic graph whose Laplacian 
 has purely singular continuous spectrum. We prove that motion remains ball
 istic along at least one layer under quite general assumptions. We constru
 ct a graph whose Laplacian has purely absolutely continuous spectrum\, exh
 ibits ballistic transport\, yet fails to satisfy a dispersive estimate. We
  believe that this class of graphs can serve as a playground to better und
 erstand exotic spectra and dynamics in the future. Based on a joint work w
 ith Joachim Kerner\, Olaf Post and Mostafa Sabri (Comm. Math. Phys.\, 2025
 ).
LOCATION:Seminar Room 2\, Newton Institute
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