The additive structure of the spectrum of a metric graph
Peter Sarnak - Institute for Advances Study
Date & time: Wednesday, 21 July 2021 at 10:45AM - 11:45PM
Abstract : A metric graph is a (finite) graph with lengths assigned to its edges, making it into a singular one-dimensional space .The spectrum of the Laplacian with Neumann conditions at the vertices is governed by the geometry of certain subvarieties of a torus, and has been exploited in works of Barra-Gaspard, Colin de Verdiere,Alon -Band -Berkolaiko ,....
The diophantine geometry of these subvarieties leads to a description of the additive structure of these spectra. They are quite rich and yield examples of exotic crystalline measures that had been long sought. Joint work with Pavel Kurasov