  We derive the explicit expression for the four-point correlation function of
stress-energy tensors in four-dimensional N=4 superconformal theory. We show
that it has a remarkably simple and suggestive form allowing us to predict a
large class of four-point correlation functions involving the stress-energy
tensor and other conserved currents. We then apply the obtained results on the
correlation functions to computing the energy-energy correlations, which
measure the flow of energy in the final states created from the vacuum by a
source. We demonstrate that they are given by a universal function independent
of the choice of the source. Our analysis relies only on N=4 superconformal
symmetry and does not use the dynamics of the theory.
