  We propose a physical system allowing one to experimentally observe the
distribution of the complex zeros of a random polynomial. We consider a
degenerate, rotating, quasi-ideal atomic Bose gas prepared in the lowest Landau
level. Thermal fluctuations provide the randomness of the bosonic field and of
the locations of the vortex cores. These vortices can be mapped to zeros of
random polynomials, and observed in the density profile of the gas.
