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SUMMARY:Spectrum of the Dirac operator in thin domains: waveguides and pla
 nar domains defined by the graph of a function
DTSTART:20260511T120000Z
DTEND:20260511T130000Z
DTSTAMP:20260502T152000Z
UID:indico-event-15273@indico.math.cnrs.fr
DESCRIPTION:Speakers: Thomas Ourmières-Bonafos (Marseille)\n\nIn this tal
 k\, we study the spectrum of the Dirac operator in planar domains equipped
  with infinite mass boundary conditions. We consider two settings: wavegui
 des and domains defined as planar regions lying below the graph of a funct
 ion. Our goal is to derive asymptotic expansions of the eigenvalues in reg
 imes where these domains become thin.\n \nWe will show how tools from sem
 iclassical analysis and pseudodifferential calculus provide a powerful fra
 mework for addressing such problems. In particular\, we employ a dimension
  reduction technique\, known as the Grushin method\, which yields an effec
 tive operator in both settings. The originality of this approach lies in t
 he fact that the symbols of the operators under consideration are operator
 -valued\, acting on functions of a single variable. Using this method\, we
  also obtain refined information on the associated eigenmodes\, including 
 elliptic estimates and microlocalization results.\n \nThis are joint work
 s with  L. Le Treust\, L. Mazzouza\, F. Monteghetti et N. Raymond.\n\nht
 tps://indico.math.cnrs.fr/event/15273/
LOCATION:Amphi Schwartz
URL:https://indico.math.cnrs.fr/event/15273/
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