Appears in collection : Symmetry in Geometry and Analysis

A pseudo-Riemannian locally symmetric space is the quotient manifold $\Gamma\backslash G/H$ of a semisimple symmetric space $G/H$ by a discontinuous group $\Gamma$. Professor Toshiyuki Kobayashi initiated the study of spectral analysis of intrinsic differential operators such as the (non-elliptic) Laplacian on a pseudo-Riemannian locally symmetric space. In particular, he presented a new direction of studying the behavior of spectral analysis under small deformations of $\Gamma\backslash G/H$ based on his deformation theory. In this talk, I would like to explain recent results about the multiplicities of stable eigenvalues of the hyperbolic Laplacian in the special setting of the anti-de Sitter manifold $\Gamma\backslash SO(2, 2)/SO(2, 1)$.