  When a torus acts on a compact oriented manifold with isolated fixed points,
the equivariant localization formula of Atiyah--Bott and Berline--Vergne
converts the integral of an equivariantly closed form into a finite sum over
the fixed points of the action, thus providing a powerful tool for computing
integrals on a manifold. An integral can also be viewed as a pushforward map
from a manifold to a point, and in this guise it is intimately related to the
Gysin homomorphism. This article highlights two applications of the equivariant
localization formula. We show how to use it to compute characteristic numbers
of a homogeneous space and to derive a formula for the Gysin map of a fiber
bundle.
