Analysis on pseudo-Riemannian locally symmetric spaces. Chern Centennial Conference. Mathematical Science Research Institute (MSRI) at Berkeley, California, USA, 30 October-5 November 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 odd-dimensional anti-de Sitter manifolds as an exmaple, I plan to illustrate some applications of Chern's ideas to the new construction of L^2 spectrum which is stable under the deformation of discontinuous groups.

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© Toshiyuki Kobayashi