Abstract:  

The quantum unique ergodicity conjecture of Rudnick and Sarnak concerns the mass equidistribution in the large eigenvalue limit of Laplacian eigenfunctions on negatively curved manifolds. This conjecture has been resolved by Lindenstrauss when this manifold is the modular surface SL_2(Z)\H. I will discuss a variant of this problem in this arithmetic setting concerning the mass equidistribution of Laplacian eigenfunctions on submanifolds of the modular surface, along with connections to period integrals of automorphic forms.