  We present a rigorous proof of the appearance of quantized vortices in dilute
trapped Bose gases with repulsive two-body interactions subject to rotation,
which was obtained recently in joint work with Elliott Lieb. Starting from the
many-body Schroedinger equation, we show that the ground state of such gases
is, in a suitable limit, well described by the nonlinear Gross-Pitaevskii
equation. In the case of axially symmetric traps, our results show that the
appearance of quantized vortices causes spontaneous symmetry breaking in the
ground state.
