@00797bc6 @47933d1d - I should have been a lot clearer: I wasn't suggesting Joe say anything false in his research statement, I just meant he should not treat it as the place to bare his heart and talk about everything he's interested in doing.  He needs to leave out most of that and focus on how his most impactful work has already transformed the landscape of applied category theory.  It's much more impressive to talk about that.

"Every time someone asks what I'm currently working on, I'm frozen because immediately I'm confronted with a list of 10+ projects I've unwisely mentally listed as "active"."

If I talked about all the projects I'm working on in a research statement, people would laugh at it: the mathematics of tuning systems and modes, the splitting principle, the moduli space of triangles, the work and life of Hoàng Xuân Sính, separable algebras in Grothendieck's Galois theory....   I would leave all that out and focus on applying category theory to modeling in epidemiology. 

 @b4c50e1b @47933d1d 
The problem is bigger - junior people who work in different areas at the same time are viewed with suspicion, or worse, by hiring committees.

(Worse - as there could be internal politics at play - if currently it's the turn of Area A to hire, but they are not on the good terms with Area B, saying that you work in both A and B will be held against you, rather than work for you. I got caught in such a situation once myself). 

 @00797bc6 wrote:

"The problem is bigger - junior people who work in different areas at the same time are viewed with suspicion, or worse, by hiring committees."

Yes.  There's a limit to how much one can pretend to be something one is not, but I try to tell my grad students that they should pick one thing to be the world's expert on, and let other things take a background role.  Joe is the world's expert on the monoidal Grothendieck construction.  That work has been used in at least two software projects involving multiple people: one when he was a grad student, and another now: I'm using that math to help design software for modeling infectious disease.   But there are also lots of other papers citing Joe's work on this!  If he explains those in his research statement, he'll look like what he truly is: the world's expert on some pure math that has lots of different applications.

@47933d1d -