new year's resolutions, of a mathematical nature.

1. learn about Riccι curvature.  this is beginning to look like one of those subjects that i can't get away with not knowing.  it seems to come up every year or so, if only as a special case of a new phenomenon in metrιc spaces.
   
   for example, if you believe this preprint, then there may be some hope for a second-order theory of sobοlev spaces, which sounds really cool ..!
   
   
2. write a paper (or two) about geοmetric measure theοry.  this is partly to convince people (including myself) that i know something about GMT ..
   
   .. though, to be fair, it will probably be from a metric space viewpoint.
   
   speaking of which, i have something written now in the form of notes, but the result isn't good enough yet.  now that i think about it ..
   
   .. edited resolution: if i don't get a better idea by vappu (1 may), then i'm submitting a final form of my write-up.
   
   
3. get a new job [1].  this isn't completely within my control, of course, but then again, nothing really is.
   
   my family has been asking where, and i've been telling them that i don't know.  it's not like it's up to me, right ?.. and it's a dangerous enough thing to want something, anyway.
   ..
   ..
   i guess it doesn't hurt to indicate a small preference: it would be nice to stay in helsinki for two years, maybe three .. if only because i like it here.  my colleagues are fine people, the city is comfortable [2] and it would be nice not to have to pack up and move again.
   
   (ye gods, i hate moving.)
   
   sometimes i watch my colleagues (the tenured and tenure-track ones) and they always seem busy with administrative tasks.  it's not that i'd say no to a decent permanent job, but:
   
   
   • i may not be that good at research, but that doesn't mean that i want to stop it;
     
     there are still a few ideas that i want to work out,
     a few problems that take a few years to solve ..
     
     .. that is, if i'm the one to solve them.
     
     
   • i still don't feel like i know anything.  right now i couldn't be anyone's advisor; i don't know my field well enough to think of ph.d. problems for the next generation ..
     
     .. so a few more years of experience would be helpful.
     
     
4. *new* work out a new proof every month. [3]  i browse through the arXιv fairly often (every monday and thursday) but apart from titles, abstracts, and introductions, i don't really get much out of it ... which is my own fault.
   
   lately i feel like i've been using the same methods, over and over again.  according to gian-carlo rota, every mathematician has only a few tricks .. which sounds dooming.
   
   maybe it's worth seeing if rota was right or wrong.  if anything, it can't hurt to read more.
   
   
5. update this blog every friday at least once a week.  lately my posts have been sparse, though i can't really tell you why.
   
   maybe it's the inevitable effect of having kept it up for so long, and that there are fewer things worth sharing.  maybe mathematics is getting less frustrating for me ..
   
   (laughs)
   well, a boy can dream, right?
   
   i could use an easy resolution, anyway.  besides, there are always the resolutions above to write about; maybe doing so will actually convince me to fulfill them .. (-:
   

[1] to those not in the know: i have nothing against my current job.  it's great, actually, but the contract is for one year only.

[2] it would help, of course, if i finally sat down and learned some finnish.  fortunately, this is a list of mathematical resolutions, so i can leave it off the list ..! (-:

[3] originally it was going to be one proof per week, but then realised that it was too unrealistic.  i might as well start off small, first.