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Scattering on a decorated star-graph as a toy model for the spectral theory of automorphic functions

Thursday 15th February 2007 - 14:30 to 15:30
INI Discussion Room

A compact Riemannian manifold of dimension less than 4 with a finite number of semi-lines attached to the manifold is considered. It is shown that there is a deep analogy between the scattering and spectral properties of Schrodinger operators for this hybrid manifold and those for the automorphic Laplacian on Riemann surfaces with cusps. As an application, a relation between the scattering amplitude for hybrid manifolds with underlying compact Riemann surfaces of constant negative curvature and the Selberg zeta-function for this surface is obtained.

Presentation Material: 
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons