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SUMMARY:The Steklov spectrum for spaces with fibred cusp boundary -  Joint
  seminar with Spectral Geometry in the Clouds - Daniel Grieser (Carl von O
 ssietzky Universität Oldenburg)
DTSTART:20260316T160000Z
DTEND:20260316T170000Z
UID:TALK245218@talks.cam.ac.uk
DESCRIPTION:The Dirichlet-Neumann operator for a compact Riemannian manifo
 ld with smooth boundary has discrete spectrum\, known as Steklov spectrum.
  This still holds if the boundary is only Lipschitz. However\, as was firs
 t analyzed by Nazarov and Taskinen\, essential spectrum appears when the b
 oundary has cusp singularities.&nbsp\;\nI will consider the more general c
 ase of fibred cusp singularities (a simple example being the domain obtain
 ed by taking a ball B and removing from it a smaller ball touching B from 
 the inside). I will give a precise description of the Schwartz kernel of t
 he Dirichlet-Neumann operator near the singularity -- it lies in an adapte
 d singular pseudodifferential calculus\, the phi-calculus of Mazzeo and Me
 lrose -- and a formula for the bottom of its essential spectrum. This is j
 oint work with K. Fritzsch and E. Schrohe.
LOCATION:Seminar Room 2\, Newton Institute
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