Graph databases and graph analytics is an emerging space (see https://news.ycombinator.com/item?id=6786563).
The best snapshot would be to read the conference proceedings from SPLASH 2013. Then you could read the last 12 month's transactions and conference papers put out by the IEEE and ACM. These sources should give you a clear picture of what is leading edge research and what the open questions are.
Good luck! and keep us on HN posted about your work.
You need to understand Bayesian statistics enough to understand this paper: http://www.stanford.edu/~ngoodman/papers/WSG-AIStats11.pdf
But seriously, I think Encryption, proof systems, and other crypto stuff continue to be important and interesting. I think part of this renewed interest is based on current events (The rise of crypto currencies, NSA leaks) but just because that has driven interest doesn't mean that their isn't interesting work being done... just the opposite.
[1] http://peekaboo-vision.blogspot.com/2013/01/machine-learning...
As an aside, I disagree with at least one of the paths to "tough luck" (in clustering). Trial and error with different #s of K helps. There is also something called x-means that might be useful.