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SUMMARY:Kirk Public Lecture: Decoding geometry from spectra - Carolyn Gord
 on (Dartmouth College)
DTSTART:20260325T160000Z
DTEND:20260325T170000Z
UID:TALK230782@talks.cam.ac.uk
DESCRIPTION:Inverse spectral geometry asks the extent to which geometric a
 nd topological information is encoded in spectral data. For geometric obje
 cts\, we will primarily consider Riemannian surfaces\, especially bounded 
 Euclidean domains. We will look at two types of spectral data: &nbsp\;the 
 spectrum of the Laplacian (with Dirichlet or Neumann boundary conditions) 
 and the Steklov spectrum\, focusing primarily on the latter. The inverse s
 pectral problem for the Laplacian is sometimes phrased as ``Can one hear t
 he shape of a drum?'' since the eigenvalues of a plane domain correspond t
 o the characteristic frequencies of vibration of the domain viewed as a vi
 brating membrane. The Steklov spectrum of a bounded domain or of a Riemann
 ian manifold M with boundary is the eigenvalue spectrum of the so-called D
 irichlet-to-Neumann operator\, which inputs smooth functions u on the boun
 dary of M and outputs the normal derivative across the boundary of the uni
 que harmonic extension of u to M.&nbsp\; The study of the Steklov spectrum
 \, first introduced in 1902\, has seen a surge of interest in recent decad
 es with striking results. &nbsp\;After introducing the spectra\, we will g
 ive a sampling of techniques\, progress and open questions.
LOCATION:Seminar Room 1\, Newton Institute
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