I am a recent PhD student trying to settle into a research topic. Even though I have a current project I am working on, I am not particularly enjoying it and would like to switch. Before braving the lion's den and telling my supervisor that I would like to change projects, I figure it would be prudent to do some research on current research.
To be more precise, I have developed a small fascination with the moduli space of flat connections on Riemann surfaces, but I do not know the current state of research in that field. I hope that my questions are not so vague as to bring down the wrath of the overflow gods, but they are as follows:
- How active is current research in the moduli space of flat connections? Some scholarly searching reveals there are still papers being published in the field, but has the research talent narrowed to specific experts?
- Is the field still in a state where it would be reasonable to do a PhD and actually get novel results in a reasonable amount of time? (I ask only because I have colleagues whose work lies in the Langland's program, and they seem to have spent the majority of their graduate careers just trying to get the point where they can ask a reasonable question.)
My apologies if the question seems infantile. It's just that there is a mountain ahead of me and I cannot seem to see past the first ridge.