Discrete Spectrum for Non-Riemannian Locally Symmetric Spaces. Cohomology of Arithmetic Groups (on the occasion of Prof. MS Raghunathan turning 70 during the year). Tata Institute of Fundamental Research, Mumbai, India, 28-31 December 2011.

I will discuss

1. discontinuous groups Γ for symmetric spaces X with indefinite metric,
2. spectral analysis of the Laplacian on X/Γ.

In this situation, the Laplacian is no more an elliptic operator.

Taking an odd dimensional ant-de Sitter manifold and a three dimensional ''indefinite projective space'' as examples, I plan to illustrate a new idea for the construction of L2 spectrum which is stable under the deformation of discontinuous groups.

[ program (pdf) ]

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