In the short term, a series of collapses as we reach ever closer toward that singularity. There's a great many constraints on our ability to grow while on Earth, and it's proving difficult to get off the planet in any reasonable method with our current technology. I suspect we'll need to fall down and rebuild a couple times before we can reliably spread to other planets, or even simply exist in orbit.

Once we get up there, though, and we're no longer constrained by Earth's resource limits, we'll grow signficantly. I suspect we'll move toward a machine-based society, both in automation and robotics, but also integrating technology into our bodies.

At some point, someone is going to figure out how to do that mind to machine transfer, and we'll diverge as a species. The organic humans and the composite AI / machine-based humanity.

Knowing how stupid we are, though, we'll probably end up becoming the Borg.