".. but i have promises to keep, and miles to go .."

.. before i slip and break them.

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i think i make too many mathematical promises to too many people. if you take my word at face value, then by the end of next week ..

1. i should have finished final edits of a preprint, chosen a journal, and submitted the preprint to it,
   
   
2. i should have written a rough draft of a new (but short) preprint,
   
   
3. i should have proven a few new lemmas/theorems,
   ready to be discussed with (separate) colleagues in the department,
   
   
4. i should have started reading this one paper and have the rough idea in mind, in preparation for a seminar talk in two weeks,
   
   
5. i should have read another paper that a colleague sent me.
   

then again, this backlog of work isn't completely dire:

1. after browsing through the outline again, it doesn't include any substantial changes. i've also narrowed down to a handful of journals; if pressed, two coin tosses can settle that decision.
   
   
2. i have some work notes already in LaTeX form, and the estimates are fleshed out. there are some technical details lacking, as well as the misery that is writing an introduction .. but it's something.
   
   
3. i've already worked out most of the details, for one theorem.
   
   
4. the talk is in two weeks, so there's still time.
   
   
5. i don't think they actually believed me when i said i would read it soon. heck, i never believe anyone, either. it's not that people are untrustworthy, but simply that people are good-intentioned yet busy. [1]
   

odds are good that i won't do everything in its entirety.

it also doesn't help that i'm taking a day off from the usual research. instead, i woke up and immediately decided to revisit some topics from to my dissertation.

as for what i learned, so far ..

the bad news: the theory of dirιchlet forms is probably not relevant, after all. it's a great theory, but like Weavεr's theory of derivatιons, the setting is quite abstract and nothing comes for "free."

it's not unlike IKEA furniture: the items are affordable, but you have to take the time and effort to build them yourself. it's one thing to have a dirichlεt form ready on your space. on the other hand, it's quite another matter to start with a space and build such an operator yourself.

the good news: i might not need the theory of dirιchlet forms, after all.

as a side note, i wish i had time to read the work of sτurm and other related authors and works. that looks like interesting, useful stuff.

anyway: back to work. the list will only grow if i don't get back to it.

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[1] also: here's a belated thanks to those of you who read my draft about the schoenflιes result and quickly came back with comments. that's item (1), above; i'll submit it soon.