We propose an experiment to explore the magnetic phase transitions in interacting fermionic Hubbard systems, and describe how to obtain the ferromagnetic phase diagram of itinerant electron systems from these observations. In addition signatures of ferromagnetic correlations in the observed ground states are found: for large trap radii (trap radius $R_T > 4$, in units of coherence length $xi$), ground states are topological in nature -- a skyrmion in 2D, and a hedgehog in 3D.
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