> it has a concave ceiling <
This is a problem because that shape focuses sound. That kind of focusing is the opposite of diffusion, which would be good.
> What are the acoustical problems i should be looking out for the most and what will the best solution be for it? <
Everything you need is right here:
www.ethanwiner.com/acoustics.html
It's a fair amount to read, but it's all in plain English. Better still, there's no math.
--Ethan