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SUMMARY:Simplicity of the Second Dirichlet Eigenvalue on Triangles: Analyt
 ical Estimates and Computer-Assisted Proof
DTSTART:20261019T123000Z
DTEND:20261019T133000Z
DTSTAMP:20261015T012500Z
UID:indico-event-17550@indico.math.cnrs.fr
DESCRIPTION:Speakers: Endo Ryoki (Durham University)\n\nThis talk presents
  a proof that the second eigenvalue of the Dirichlet Laplacian is simple\n
 on every non-equilateral triangle\, thereby resolving a conjecture of Laug
 esen and\nSiudeja. The proof combines analytical estimates with verified n
 umerical computation.\nThe principal difficulties arise near the equilater
 al configuration\, where the second and\nthird eigenvalues coalesce\, and 
 in the nearly degenerate regime\, where the eigenvalues\ndiverge. A differ
 ence-quotient formulation based on the Hadamard shape derivative\nprovides
  rigorous control of eigenvalue splitting near the equilateral triangle. F
 or nearly\ndegenerate triangles\, suitable eigenvalue bounds are obtained 
 through comparison with\none-dimensional Schrödinger operators. Together 
 with verified finite element computations\,\nthese estimates establish sim
 plicity for the entire class of non-equilateral triangles.\nThis is joint 
 work with Xuefeng Liu.\n\nhttps://indico.math.cnrs.fr/event/17550/
LOCATION:313 (Site des Carmes)
URL:https://indico.math.cnrs.fr/event/17550/
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