Alexander Veselov (Loughborough University)
A.P.Veselov@lboro.ac.uk The spectral problem of three-dimensional manifolds admitting Sol-geometry in Thurston's sense will be discussed. Topologically such a manifold is a torus bundle over a circle with unimodular hyperbolic gluing map. We will show that the spectrum of the corresponding Laplace-Beltrami operator is degenerate and the multiplicities are directly related to the number of representations of an integer by a given indefinite binary quadratic form.
The talk is based on a recent work by A. Bolsinov, H. Dullin and the speaker.