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).
"Spectral analysis on pseudo-Riemannian locally symmetric spaces." Proc. Japan Acad. Ser. A Math. Sci. 96 (8) 69 - 74, October 2020. https://doi.org/10.3792/pjaa.96.013