One of the things I’ve been spending a lot of time on mathematically is problems around representation stability and “FI-modules,” joint with Tom Church, Benson Farb, and Rohit Nagpal. Benson just talked about this stuff at the ICM, and here it is:
In the latest stable representation theory news, Andy Putman and (new Wisconsin assistant professor!) Steven Sam have just posted an exciting new preprint about the theory of representations of GL_n(F_p) as n goes to infinity; this is kind of like the linear group version of what FI-modules does for symmetric groups. (Or, if you like, our thing is their thing over the field with one element….!) This is something we had hoped to understand but got very confused about, so I’m looking forward to delving into what Andy and Steven did here — expect more blogging! In particular, they prove the Artinian conjecture of Lionel Schwartz. Like I said, more on this later.