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SUMMARY:The Essential Spectrum of the Neumann-Poincaré Operator on Highly
  Oscillatory Boundaries - Simon Chandler-Wilde (University of Reading)
DTSTART:20260414T130000Z
DTEND:20260414T140000Z
UID:TALK244003@talks.cam.ac.uk
DESCRIPTION:This talk is concerned with the numerical verification\, or ot
 herwise\, of a conjecture in spectral geometry due to Kenig\, that the spe
 ctral radius of the Neumann-Poincar&eacute\; operator\, i.e.\, the double-
 layer potential operator in potential theory\, is < 1/2 for every bounded 
 Lipschitz domain\, equivalently that the same holds for the essential spec
 tral radius.&nbsp\; We study this conjecture in two space dimensions for a
  class of highly oscillatory piecewise analytic boundaries for which we ca
 n compute numerical approximations to the essential spectrum and functiona
 ls that determine whether the essential spectral radius is < 1/2 at a cont
 inuous level. The tools are a Floquet-Bloch transform\, the trapezoidal ru
 le and Nystrom method for analytic functions and associated error estimate
 s\, and new (but rather straightforward) Banach space estimates for the sp
 ectral radius of an operator in terms of computable quantities for operato
 r approximations. This is joint work with Raffael Hagger (Kiel)\, Karl-Mic
 hael Perfekt (Trondheim)\, and Jani Virtanen (Reading/Eastern Finland).&nb
 sp\; &nbsp\;
LOCATION:Seminar Room 1\, Newton Institute
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