  The equation of state of a weakly interacting two-dimensional Bose gas is
studied at zero temperature by means of quantum Monte Carlo methods. Going down
to as low densities as na^2 ~ 10^{-100} permits us for the first time to obtain
agreement on beyond mean-field level between predictions of perturbative
methods and direct many-body numerical simulation, thus providing an answer to
the fundamental question of the equation of state of a two-dimensional dilute
Bose gas in the universal regime (i.e. entirely described by the gas parameter
na^2). We also show that the measure of the frequency of a breathing collective
oscillation in a trap at very low densities can be used to test the universal
equation of state of a two-dimensional Bose gas.
