Spectral analysis on pseudo-Riemannian locally symmetric spaces

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