There are only a limited number of conceivable ways of staying off the ground. There are lighter-than air aircraft, there are aircraft where lift is provided by the flow of air over an airfoil, there are rockets where lift comes from the reaction force of expelling rocket fuel, there are ballistic projectiles that are kept aloft by previously supplied momentum, and there are levitated objects kept aloft by externally applied force. That may be an exhaustive list of all ways of flying ever imagined, until yesterday.
A solid object may be kept aloft by a difference in pressure between its upper and lower surfaces, with the total upward pressure being greater than the total downward pressure by an amount sufficient to compensate for the weight of the object. Practically, this means that either it's lighter than air and the pressure difference is hydrostatic, or it's moving and the pressure difference is hydrodynamic. However, there is a third possibility: the pressure difference is hydrostatic, and the air can't get around the object at a significant rate.
My invention is simply several square kilometers of plastic sheet, some means of keeping it spread out and level, and a few air pumps. Air is pumped through as needed to keep up with the flow of air around the edges. The simplest means of keeping it spread out is probably rotation. Alternatively, the air being pumped through could be released in angled jets to maintain conformation, or air could be pumped through at controlled locations so that the pressure difference is greatest in the middle and the rest of the sheet hangs down slightly under tension. That last option would presumably require especially precise control.