the quantum unique ergodicity conjecture of rudnick and sarnak says that eigenfunctions of the laplacian on a compact manifold of negative curvature become equidistributed as the eigenvalue tends to infinity. in the talk, i will discuss recent work on this problem for arithmetic quotients of the three-dimensional hyperbolic space. i will discuss our key result that hecke eigenfunctions cannot concentrate on certain proper submanifolds. joint work with lior silberman.