We give an overview of some new and old results on geometric properties of eigenfunctions
of Laplacians on Riemannian manifolds. We discuss properties of nodal sets and critical …

For a large class of quantized ergodic flows the quantum ergodicity theorem states that
almost all eigenfunctions become equidistributed in the semiclassical limit. In this work we …

We calculate the quantum variance for the modular surface. This variance, introduced by S.
Zelditch, describes the fluctuations of a quantum observable. The resulting quadratic form is …

We give an overview of some old results on weak* limits of eigenfunctions and prove some
new ones. We first show that on M=(S n, can) every probability measure on S* M which is …

It is well known that (i) for every irrational number α the Kronecker sequence m α (m= 1,..., M)
is equidistributed modulo one in the limit → ∞, and (ii) closed horocycles of length ℓ become …

In this paper we study quantum variance for the modular surface X= Γ \ H, where Γ= SL_2 (Z)
is the full modular group. We evaluate asymptotically the quantum variance, which is …

Rigidity of multiparameter actions Page 1 ISRAEL JOURNAL OF MATHEMATICS 149 (2005),
199-226 RIGIDITY OF MULTIPARAMETER ACTIONS BY ELON LINDENSTRAUSS Department …

We discuss dynamical properties of actions of diagonalizable groups on locally
homogeneous spaces, particularly their invariant measures, and present some number …

A method for determining quantum variance asymptotics on compact quotients attached to
non-split quaternion algebras is developed in general and applied to" microlocal lifts" in the …

It is a folklore result in arithmetic quantum chaos that quantum unique ergodicity on the
modular surface with an effective rate of convergence follows from subconvex bounds for …