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SUMMARY:The arithmetic structure of the spectrum of a metric graph - Peter
  Sarnak (Princeton University)
DTSTART:20240411T143000Z
DTEND:20240411T153000Z
UID:TALK214015@talks.cam.ac.uk
DESCRIPTION:Endowing a finite combinatorial graph with lengths on&nbsp\;it
 s edges defines singular 1-dimensional Riemannian manifolds&nbsp\;known as
  metric graphs. The spectra of their Laplacians have been&nbsp\;widely stu
 died.We show that these spectra have a structured linear&nbsp\;part descri
 bed in terms of arithmetic progressions and a nonlinear&nbsp\;"random" par
 t which is highly linearly and even algebraically independent&nbsp\;over t
 he rationals.These spectra give rise to exotic crystalline measures&nbsp\;
 and resolve various open problems concerning them.\nJoint work with Pavel 
 Kurasov.
LOCATION:Seminar Room 1\, Newton Institute
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