I'm working on tightening the bounds on the Jordan-Schur theorem. I've improved the best known bounds but not by much. If this project does succeed it might end up turning into my PhD thesis.
Out of idle curiosity (I haven't studied any proof of the Jordan-Schur theorem), are you doing that by tuning up the existing proofs of best bounds through more careful analysis, by replacing relatively large chunks of those proofs by new arguments, or by employing an altogether new proof?
Whpearson recently mentioned that people in some other online communities frequently ask "what are you working on?". I personally love asking and answering this question. I made sure to ask it at the Seattle meetup. However, I don't often see it asked here in the comments, so I will ask it:
What are you working on?
Here are some guidelines