The question whether there exists finite-volume hyperbolic Riemann surfaces with very few Laplaceeigenvalues is related to the conjecture that the eigenvalues of the Laplacian should have an upper bound on the multiplicity for congruence Riemann surface, i.e, $=\Gamma\backslash H$ for $\Gamma$ being a congruence subgroup.

Also Lindenstrauss proved important results in ergodic theory, which were crucial in the proof of the Quantum unique ergodicity conjecture proven Soundararajan.
http://www.aimath.org/~kaur/RecentProgressQUE2(901).pdf