How to identify future directions in a saturated field without getting discouraged I am close to finishing a PhD in applied mathematics and I'm looking to develop future projects that go beyond my dissertation topic into other domains.  One of the major subjects my advisor has suggested that I look into is an extremely saturated - but still largely "unresolved" - field.  While I find the subject incredibly fascinating and challenging, I am also intimidated by the amount of work that has already been done, and I worry that I might loose the niche I've dug out for my dissertation by trying to play in someone else's big pool.  I feel like I might have something to contribute, if nothing else from a "translational/interdisciplinary" perspective (applying the expertise gained during my PhD to a different field), but is there a good way to feel out where exactly I fit in?  I suppose a logical answer to my own question would be to identify a post-doc position with a leading group in the field, but I am interested in hearing other opinions.
If you browse through top 10 schools (or researchers') websites, you might get a "feeling" on where (or what) their research is heading towards! For example, you can check what their newest post docs are working on, PhD students' thesis titles etc. You can also do the same thing by checking NSF newly funded proposals. This may not give you a definite answer, but it might help you establish a "directional sense"

PS.
I'm in engineering not math.