  Given a Riemannian manifold endowed with its Laplace-Beltrami operator,
consider the associated spectral projector on a thin interval. As an operator
from L2 to Lp, what is its operator norm? For a window of size 1, this question
is fully answered by a celebrated theorem of Sogge, which applies to any
manifold. For smaller windows, the global geometry of the manifold comes into
play, and connections to a number of mathematical fields (such as Differential
Geometry, Combinatorics, Number Theory) appear, but the problem remains mostly
open. The aim of this article is to review known results, focusing on cases
exhibiting symmetry and emphasizing harmonic analytic rather than microlocal
methods.
