In this talk, we discuss the relation, on a locally symmetric space of higher rank and infinite volume, between the bottom of the $L^2$-spectrum of the Laplace–Beltrami operator and the convergence rate of the discrete subgroup. We also discuss their implications for the Strichartz inequality, a fundamental tool in the study of nonlinear dispersive equations.

The video of this talk is available on the IISc Math Department channel.