on exposition.

since october i've been repeating this mantra: in december, i'll have my life back. by then i'll be a mathematician again.

(this was in regards to job applications, research travels, and other promises i meant to keep.)

to be fair, i was half-right. there is still one survey article to finish ..

.. but being more to do with research than, say, a statement of teachιng philosophy, i don't mind it at all. in fact, i'm enjoying it.

for one thing, writing makes me feel like i know something well.

it's been more than a year and 1/2 since i first worked out these details regarding de giοrgi's approach to reguΙarity theory (for certain ellιptic PDE) and only now does it feel .. natural.

that's the feeling, anyway: let's see if i can convince others of the same, through this article ..

the more i think about it, the more i like this idea of writing notes and expositions. in this last conference at οberwolfach, i was struck by the clarity of the research notes that colleagues of mine had written.

this is in regards to a generalised radεmacher theorem, in the setting of certain metrιc measure spaces.

the first proof was quite hard. there's a history of several versions of notes by several authors, in efforts to understand this result.

i liken it, actually, to how anyone in the open-source software community can contribute code for a particular program task. on the other hand, the best code gets passed around and used, for the greater good.

so i'm tempted to write my own notes on other subjects. specifically, there are a lot of folklore theorems out there, in this intersection between analysιs on metric spaces and geοmetric measure theory.

i could be deluding myself into thinking that my perspective is overly valuable .. but maybe by expositing, i can help as others have helped me.