  Motivated by the first experimental evidence of ferromagnetic behavior in a
three-dimensional ultracold atomic gas, we explore the possibility of itinerant
ferromagnetism in a trapped two-dimensional atomic gas. Firstly, we develop a
formalism that demonstrates how quantum fluctuations drive the ferromagnetic
reconstruction first order, and consider the consequences of an imposed
population imbalance. Secondly, we adapt this formalism to elucidate the key
experimental signatures of ferromagnetism in a realistic trapped geometry.
