Abstract

I plan to discuss a new theory for spectral analysis of pseudo-Riemannian locally symmetric spaces, aiming to extend beyond the traditional Riemannian framework. I will illustrate new phenomena arising from indefinite metrics. Recent advancements in overcoming challenges in global analysis with indefinite metrics have been achieved through developments in the branching theory of infinite-dimensional representations of reductive groups, which rely on geometries featuring hidden spherical symmetries. I aim to elucidate non-technical but crucial ideas during the lecture.