Quantum unique ergodicity for ${\rm SL}_2(\mathbb{Z})\backslash\mathbb{H}$

Abstract

We eliminate the possibility of “escape of mass” for Hecke-Maass forms of large eigenvalue for the modular group. Combined with the work of Lindenstrauss, this establishes the Quantum Unique Ergodicity conjecture of Rudnick and Sarnak for Hecke-Maass forms on the modular surface ${\rm SL}_2(\mathbb{Z})\backslash \mathbb{H}$.