I am a second year PhD student, and I still don't have an advisor. I chose this school because it has a ton of people working in the sub-field I am interested in (Mathematical Optimization). I tried lab rotations with three of the 'stars' here, but they didn't work out - two were busy during the quarter and didn't give me a problem to work on, the third one, though so far sufficiently satisfied by my work, has almost a year-long 'testing period' before taking on students, which is too long for me (I only got to know this mid-way through the last quarter).
So I relaxed my constraints and talked to professors working in a slightly different field (Control Theory), and they are willing to take me, but this means I might be doing something a bit different than what I had imagined when I came here.
Before coming to school, I was working in the industry for three years, earning a decent amount of money. I already had a Master's before that. I came back to grad school only because I wanted to work on Optimization problems and do algorithm analysis for them. Now I might have to do modeling of problems in Control Theory. The mathematics at the heart of the two fields is quite different, and I already spent a whole year taking hardcore Optimization and Convex Analysis classes (which I now feel will be a waste).
All this is making me depressed. Quitting is absolutely not an option for me.
My question is this - do people do one thing and then end up getting back on track doing what they really want to do? Is this even possible? Especially if what you really want to do is math-intensive.
EDIT, March 2017 : In case some other PhD student comes in reading this, I can imagine what you are going through with all your 'failed' rotations. Just wanted to say, I tried a rotation with a 'star' in my field of interest (Optimization) one last (fourth) time. And he has now agreed to be my advisor! :) :) :) :) :) :) :) I won't have to compromise after all, and I am so, so, so happy.