PDE-MP-HA seminar, 4th April 2008, 1:50pm, Bloc627

Speaker: Gregory Berkolaiko, Texas A&M
Title: Relationship between scattering matrix and spectrum 
of quantum graphs


Abstract:
  Quantum graphs are usually introduced either through the
  differential operator acting on the functions defined on the edges
  of a graph or through directly specifying the scattering matrices at
  the vertices of the graphs.  This gives rise to two types of spectra
  and, therefore, two possible ways to compute spectral statistics.
  Thus obtained statistics have been long presumed to be equivalent,
  albeit without any rigorous justification.

  We will discuss the limits in which the two types of spectral
  statistics of a graph are indeed equivalent.  The result is based on
  the ergodicity of the irrational linear flow on the torus.

  The talk is based on the joint work with Brian Winn.