Micro-polymath

As usual, I've been discussing what topic to cover for this semester's research seminar with my students. We usually cover some advanced topic, or a topic that people should know that no one teaches in our department. Students give presentations, I try to foster discussion (and grumble about the presentation style), and hopefully people learn something.

This semester we have decided to try something different. With my students and my postdoc Jeff Phillips (HIRE HIM! He's GREAT ! and needs a job !), the plan is to try a polymath-style enterprise. Specifically, we made up a list of problems that satisfy the following criteria:

• The problem is interesting enough in core theory-land that a solution almost guarantees a paper without having to worry about motivation, marketing, etc etc. 
• The problem has been around and is reasonably difficult, so it's not likely to yield a solution immediately
• There's some new idea/paper/line of attack that has emerged (either because I thought of it, or someone else in our group did) that might be fruitful

This last point is very handy to whittle down the set of problems, because there's no shortage of open problems but very few of them might be amenable to attack at this point without new ideas. 

We then went over each problem and voted, picking a winner. Luckily the winning problem was a consensus winner, so everyone is hopefully motivated to work on it. 

Of course you're waiting for the punchline: which problem did we pick ? Alas, I'm not going to give that out yet. Not because of paranoia on my part, but because I'd like the students to have a certain amount of mind-space to maneuver in without having to worry about the competition. I anticipate complaints over this :).

What I ideally hope to report on a few months from now is an actual solution to the problem. Failing that I'll at least report on the progress made, and how this 'micropolymath' concept worked out.