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SUMMARY:Paul Hege: Computing spectra and proving gaps in systems with fini
 te local complexity
DTSTART:20251212T083000Z
DTEND:20251212T110000Z
DTSTAMP:20260426T034800Z
UID:indico-event-15722@indico.math.cnrs.fr
DESCRIPTION:Speakers: Paul Hege\n\nComputing operator spectra for infinite
 -volume physical systems is fundamental for understanding condensed matter
  systems numerically. But exact computation of spectral bands is presently
  only possible for periodic systems\, while less regular systems\, for exa
 mple quasicrystals or amorphous materials\, are generally studied numerica
 lly by considering a finite patch only. But adding a boundary to the syste
 m and considering of only a particular finite part both can produce uncont
 rolled errors in the computed result. In general\, these errors do not eve
 n converge to zero as the patch size increases. To make computations with 
 controlled error possible\, we present new methods for the computation of 
 spectra in a general class of physical models with finite local complexity
 \, which includes most quasicrystalline and many other systems. These meth
 ods allow for the computation of spectra with two-sided error control\, al
 lowing us to establish both the existence and the absence of spectrum (spe
 ctral gaps) formally based on concrete numerical computations. We then use
  similar methods to show that the spectrum of infinite-volume systems with
  finite local complexity is algorithmically computable\, a question for wh
 ich only negative results in the general case were previously known. This 
 is joint work with Massimo Moscolari and Stefan Teufel.\n\nhttps://indico.
 math.cnrs.fr/event/15722/
LOCATION:435 (ENS Lyon)
URL:https://indico.math.cnrs.fr/event/15722/
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