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.
[ video ]
© Toshiyuki Kobayashi