Quote Originally Posted by SE
Able to manipulate the vital energies of the land, the air, and living beings, they manifest their power through the weaving of signs, unleashing a wide array of attacks against their foes. Master the arts of the ninja and learn to bend the tide of battle to your will.
Sounds like one of the classes, at the very least, will be Arcanist (Signs sound a lot like the geometric maths they use) or, more likely, Conjurer (Stone, Aero, and 'Living Beings' are there hat).

As for the melee class they will almost certainly get their stuff from, Pugilist makes sense. But then again, Summoners and Black mages get Archer moves. So who knows?