F. Kassel and T. Kobayashi, Spectral analysis on pseudo-Riemannian locally symmetric spaces, Proc. Japan Acad. Ser. A Math. Sci. 96 (2020), no. 8, 69-74, doi: 10.3792/pjaa.96.013. arXiv: 2001.03292..

We summarize and announce some recent results initiating spectral analysis on pseudo-Riemannian locally symmetric spaces $\Gamma \backslash G/H$, beyond the classical setting where $H$ is compact (e.g. theory of automorphic forms for arithmetic $\Gamma$) or $\Gamma$ is trivial (e.g. Plancherel-type formula for semisimple symmetric spaces).