Equidistribution of lifts on Hyperbolic 4-manifolds

The quantum unique ergodicity (QUE) conjecture of Rudnick and Sarnak says that the L^2 mass of eigenfunctions of the Laplacian in hyperbolic manifolds equidistributes, as the eigenvalues tend to infinity. We consider a special class of such functions, Hecke—Maass forms, that are central in number theory. The conjecture has been established for these functions in dimension 2 and 3, but in dimension 4 there is a new challenge: one needs to rule out concentration of measure along certain large totally geodesic submanifolds. We will discuss our recent result in which we overcome this difficulty for a particular sequence of eigenfunctions known in number theory as lifts. This is a joint work with Alexandre de Faveri.