Algebraic Geometry is my answer.

As for how I'd measure it, ideally I'd look at what course has been the most frequently added as new to graduate level courses in research universities. Those topics may not be pumping out papers right this moment, but I think it would be the most accurate way to see which direction research is heading. It's also why I'd answer algebraic geometry, it's caught on like wildfire in the last few years and I've seen a few new courses on it at various universities in my area.